Tools for Crystal Symmetry Analysis¶
Crystallographic symmetry analysis which can be necessary to interpret EBSD data can be carried out using the pymatgen (“Python Materials Genomics”) library [1].
The crystallographic analysis of the structure data is provided in pymatgen via the powerful spglib library, which also defines the crystallographic conventions used in space group analysis.
Pymatgen includes routines to access crystal structure data in various input formats, including data import directly from the online Crystallography Open Database.
[1] Shyue Ping Ong, William Davidson Richards, Anubhav Jain, Geoffroy Hautier, Michael Kocher, Shreyas Cholia, Dan Gunter, Vincent Chevrier, Kristin A. Persson, Gerbrand Ceder. Python Materials Genomics (pymatgen) : A Robust, Open-Source Python Library for Materials Analysis. Computational Materials Science, 2013, 68, 314–319. doi:10.1016/j.commatsci.2012.10.028
[1]:
import numpy as np
import pymatgen as mg
from pymatgen.io.cif import CifParser
from pymatgen.ext.cod import COD
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer
Importing Structure Data¶
[2]:
#this gets the primitive cell
parser = CifParser("Cu-Copper.cif")
prim_structure = parser.get_structures()[0]
print(prim_structure)
Full Formula (Cu1)
Reduced Formula: Cu
abc : 2.556163 2.556163 2.556163
angles: 60.000000 60.000000 60.000000
Sites (1)
# SP a b c
--- ---- --- --- ---
0 Cu 0 0 0
[3]:
cod = COD()
cod_structure = cod.get_structure_by_id(1010064)
print(cod_structure)
Full Formula (Li8 O4)
Reduced Formula: Li2O
abc : 4.610000 4.610000 4.610000
angles: 90.000000 90.000000 90.000000
Sites (12)
# SP a b c
--- ---- ---- ---- ----
0 Li+ 0.25 0.25 0.25
1 Li+ 0.25 0.75 0.75
2 Li+ 0.75 0.25 0.75
3 Li+ 0.75 0.75 0.25
4 Li+ 0.75 0.75 0.75
5 Li+ 0.75 0.25 0.25
6 Li+ 0.25 0.75 0.25
7 Li+ 0.25 0.25 0.75
8 O2- 0 0 0
9 O2- 0 0.5 0.5
10 O2- 0.5 0 0.5
11 O2- 0.5 0.5 0
[4]:
# Reading a structure from CIF
#structure = mg.Structure.from_str(open("CsCl.cif").read(), fmt="cif")
structure = mg.Structure.from_file("Cu-Copper.cif")
print(structure)
Full Formula (Cu4)
Reduced Formula: Cu
abc : 3.614960 3.614960 3.614960
angles: 90.000000 90.000000 90.000000
Sites (4)
# SP a b c
--- ---- --- --- ---
0 Cu 0 0 0
1 Cu 0 0.5 0.5
2 Cu 0.5 0 0.5
3 Cu 0.5 0.5 0
Space Group Assignment¶
[5]:
finder = SpacegroupAnalyzer(structure)
print("The space group symbol is {}".format(finder.get_space_group_symbol()))
print("The point group symbol is {}".format(finder.get_point_group_symbol()))
#structure=finder.get_symmetrized_structure()
#structure =finder.get_conventional_standard_structure()
#print(structure)
The space group symbol is Fm-3m
The point group symbol is m-3m
We can output a dictionary of all the symmetry data that has been determined by SpacegroupAnalyzer via spglib:
[6]:
symdata=finder.get_symmetry_dataset()
print(symdata)
{'number': 225, 'hall_number': 523, 'international': 'Fm-3m', 'hall': '-F 4 2 3', 'choice': '', 'transformation_matrix': array([[ 1.00000000e+00, 3.79646512e-17, 0.00000000e+00],
[ 1.91466924e-19, 1.91466924e-19, -1.00000000e+00],
[ 0.00000000e+00, 1.00000000e+00, 0.00000000e+00]]), 'origin_shift': array([ 1., 1., 1.]), 'rotations': array([[[ 1, 0, 0],
[ 0, 1, 0],
[ 0, 0, 1]],
[[-1, 0, 0],
[ 0, -1, 0],
[ 0, 0, -1]],
[[ 0, 0, 1],
[ 0, 1, 0],
[-1, 0, 0]],
...,
[[ 0, 0, 1],
[ 1, 0, 0],
[ 0, -1, 0]],
[[ 1, 0, 0],
[ 0, 0, -1],
[ 0, 1, 0]],
[[-1, 0, 0],
[ 0, 0, 1],
[ 0, -1, 0]]], dtype=int32), 'translations': array([[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 1.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 0.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[ 0.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 0.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 0.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 0.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 0.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 0.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 0.00000000e+00],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 4.44089210e-16],
[ 1.00000000e+00, 0.00000000e+00, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 0.00000000e+00, 0.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 0.00000000e+00, 0.00000000e+00, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 0.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 4.44089210e-16],
[ 0.00000000e+00, 0.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 0.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 0.00000000e+00, 0.00000000e+00, 4.44089210e-16],
[ 1.00000000e+00, 1.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 0.00000000e+00, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 0.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 0.00000000e+00, 0.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 4.44089210e-16],
[ 1.00000000e+00, 0.00000000e+00, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 1.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 0.00000000e+00, 5.00000000e-01],
[ 0.00000000e+00, 0.00000000e+00, 4.44089210e-16],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 0.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 0.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 0.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 0.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 0.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 5.00000000e-01, 1.00000000e+00, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 0.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01],
[ 5.00000000e-01, 5.00000000e-01, 4.44089210e-16],
[ 1.00000000e+00, 5.00000000e-01, 5.00000000e-01]]), 'wyckoffs': ['a', 'a', 'a', 'a'], 'equivalent_atoms': array([0, 0, 0, 0], dtype=int32), 'mapping_to_primitive': array([0, 0, 0, 0], dtype=int32), 'std_lattice': array([[ 3.61496, 0. , 0. ],
[ 0. , 3.61496, 0. ],
[ 0. , 0. , 3.61496]]), 'std_types': array([1, 1, 1, 1], dtype=int32), 'std_positions': array([[ 0. , 0. , 0. ],
[ 0. , 0.5, 0.5],
[ 0.5, 0. , 0.5],
[ 0.5, 0.5, 0. ]]), 'std_mapping_to_primitive': array([0, 0, 0, 0], dtype=int32), 'pointgroup': 'm-3m'}
Getting the unique point group operators:
[7]:
pg = np.array([ [[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]] ] )
for idx,op in enumerate(symdata['rotations']):
is_new_op=True
for pg_op in pg:
if np.array_equal(pg_op,op):
is_new_op=False
if is_new_op:
pg=np.append(pg,[op],axis=0)
#print(pg)
print(pg.shape)
(48, 3, 3)
[8]:
hkl=np.array([1,0,0])
new_hkl=np.matmul(hkl,pg)
print(new_hkl.shape)
print(new_hkl)
(48, 3)
[[ 1. 0. 0.]
[-1. 0. 0.]
[ 0. 0. 1.]
[ 0. 0. -1.]
[-1. 0. 0.]
[ 1. 0. 0.]
[ 0. 0. -1.]
[ 0. 0. 1.]
[ 1. 0. 0.]
[-1. 0. 0.]
[ 0. 0. 1.]
[ 0. 0. -1.]
[-1. 0. 0.]
[ 1. 0. 0.]
[ 0. 0. -1.]
[ 0. 0. 1.]
[ 0. 1. 0.]
[ 0. -1. 0.]
[ 0. 1. 0.]
[ 0. -1. 0.]
[ 0. 1. 0.]
[ 0. -1. 0.]
[ 0. 1. 0.]
[ 0. -1. 0.]
[ 0. -1. 0.]
[ 0. 1. 0.]
[ 0. -1. 0.]
[ 0. 1. 0.]
[ 0. -1. 0.]
[ 0. 1. 0.]
[ 0. -1. 0.]
[ 0. 1. 0.]
[ 0. 0. -1.]
[ 0. 0. 1.]
[ 1. 0. 0.]
[-1. 0. 0.]
[ 0. 0. 1.]
[ 0. 0. -1.]
[-1. 0. 0.]
[ 1. 0. 0.]
[ 0. 0. 1.]
[ 0. 0. -1.]
[-1. 0. 0.]
[ 1. 0. 0.]
[ 0. 0. -1.]
[ 0. 0. 1.]
[ 1. 0. 0.]
[-1. 0. 0.]]
[9]:
# sort out the unique hkls of the family
hkl_family=np.array([new_hkl[0]])
for idx,hkl in enumerate(new_hkl):
is_new_hkl=True
for f in hkl_family:
if np.array_equal(hkl,f):
is_new_hkl=False
if is_new_hkl:
hkl_family=np.append(hkl_family,[hkl],axis=0)
print(hkl_family.shape)
print(hkl_family)
(6, 3)
[[ 1. 0. 0.]
[-1. 0. 0.]
[ 0. 0. 1.]
[ 0. 0. -1.]
[ 0. 1. 0.]
[ 0. -1. 0.]]
[10]:
# alternative approach
# returns a list of SymmOp objects
pg_ops=finder.get_point_group_operations()
hkl=np.array([0,0,1])
family=np.array([hkl])
for idx,op in enumerate(pg_ops):
new_hkl=pg_ops[idx].apply_rotation_only(hkl)
hkl_is_new=True
for fvec in family:
if np.array_equal(new_hkl,fvec):
hkl_is_new=False
if hkl_is_new:
family=np.append(family,[new_hkl],axis=0)
print(hkl, " family:")
print(family)
[0 0 1] family:
[[ 0. 0. 1.]
[ 0. 0. -1.]
[ 1. 0. 0.]
[-1. 0. 0.]
[ 0. -1. 0.]
[ 0. 1. 0.]]
spglib Examples¶
[11]:
import sys
import spglib
import numpy as np
#######################################
# Uncomment to use Atoms class in ASE #
#######################################
# from ase import Atoms
#######################################################################
# Using the local Atoms-like class (BSD license) where a small set of #
# ASE Atoms features is comaptible but enough for this example. #
#######################################################################
from atoms import Atoms
[12]:
def show_symmetry(symmetry):
for i in range(symmetry['rotations'].shape[0]):
print(" --------------- %4d ---------------" % (i + 1))
rot = symmetry['rotations'][i]
trans = symmetry['translations'][i]
print(" rotation:")
for x in rot:
print(" [%2d %2d %2d]" % (x[0], x[1], x[2]))
print(" translation:")
print(" (%8.5f %8.5f %8.5f)" % (trans[0], trans[1], trans[2]))
def show_lattice(lattice):
print("Basis vectors:")
for vec, axis in zip(lattice, ("a", "b", "c")):
print("%s %10.5f %10.5f %10.5f" % (tuple(axis,) + tuple(vec)))
def show_cell(lattice, positions, numbers):
show_lattice(lattice)
print("Atomic points:")
for p, s in zip(positions, numbers):
print("%2d %10.5f %10.5f %10.5f" % ((s,) + tuple(p)))
[13]:
silicon_ase = Atoms(symbols=['Si'] * 8,
cell=[(4, 0, 0),
(0, 4, 0),
(0, 0, 4)],
scaled_positions=[(0, 0, 0),
(0, 0.5, 0.5),
(0.5, 0, 0.5),
(0.5, 0.5, 0),
(0.25, 0.25, 0.25),
(0.25, 0.75, 0.75),
(0.75, 0.25, 0.75),
(0.75, 0.75, 0.25)],
pbc=True)
silicon = ([(4, 0, 0),
(0, 4, 0),
(0, 0, 4)],
[(0, 0, 0),
(0, 0.5, 0.5),
(0.5, 0, 0.5),
(0.5, 0.5, 0),
(0.25, 0.25, 0.25),
(0.25, 0.75, 0.75),
(0.75, 0.25, 0.75),
(0.75, 0.75, 0.25)],
[14,] * 8)
silicon_dist = ([(4.01, 0, 0),
(0, 4, 0),
(0, 0, 3.99)],
[(0.001, 0, 0),
(0, 0.5, 0.5),
(0.5, 0, 0.5),
(0.5, 0.5, 0),
(0.25, 0.25, 0.251),
(0.25, 0.75, 0.75),
(0.75, 0.25, 0.75),
(0.75, 0.75, 0.25)],
[14,] * 8)
silicon_prim = ([(0, 2, 2),
(2, 0, 2),
(2, 2, 0)],
[(0, 0, 0),
(0.25, 0.25, 0.25)],
[14, 14])
rutile = ([(4, 0, 0),
(0, 4, 0),
(0, 0, 3)],
[(0, 0, 0),
(0.5, 0.5, 0.5),
(0.3, 0.3, 0.0),
(0.7, 0.7, 0.0),
(0.2, 0.8, 0.5),
(0.8, 0.2, 0.5)],
[14, 14, 8, 8, 8, 8])
rutile_dist = ([(3.97, 0, 0),
(0, 4.03, 0),
(0, 0, 3.0)],
[(0, 0, 0),
(0.5001, 0.5, 0.5),
(0.3, 0.3, 0.0),
(0.7, 0.7, 0.002),
(0.2, 0.8, 0.5),
(0.8, 0.2, 0.5)],
[14, 14, 8, 8, 8, 8])
a = 3.07
c = 3.52
MgB2 = ([(a, 0, 0),
(-a/2, a/2*np.sqrt(3), 0),
(0, 0, c)],
[(0, 0, 0),
(1.0/3, 2.0/3, 0.5),
(2.0/3, 1.0/3, 0.5)],
[12, 5, 5])
a = [3., 0., 0.]
b = [-3.66666667, 3.68178701, 0.]
c = [-0.66666667, -1.3429469, 1.32364995]
niggli_lattice = np.array([a, b, c])
[14]:
print("[get_spacegroup]")
print(" Spacegroup of Silicon is %s." % spglib.get_spacegroup(silicon))
print('')
print("[get_spacegroup]")
print(" Spacegroup of Silicon (ASE Atoms-like format) is %s." %
spglib.get_spacegroup(silicon_ase))
print('')
print("[get_spacegroup]")
print(" Spacegroup of Rutile is %s." % spglib.get_spacegroup(rutile))
print('')
print("[get_spacegroup]")
print(" Spacegroup of MgB2 is %s." % spglib.get_spacegroup(MgB2))
print('')
print("[get_symmetry]")
print(" Symmetry operations of Rutile unitcell are:")
print('')
symmetry = spglib.get_symmetry(rutile)
show_symmetry(symmetry)
print('')
print("[get_symmetry]")
print(" Symmetry operations of MgB2 are:")
print('')
symmetry = spglib.get_symmetry(MgB2)
show_symmetry(symmetry)
print('')
print("[get_pointgroup]")
print(" Pointgroup of Rutile is %s." %
spglib.get_pointgroup(symmetry['rotations'])[0])
print('')
dataset = spglib.get_symmetry_dataset( rutile )
print("[get_symmetry_dataset] ['international']")
print(" Spacegroup of Rutile is %s (%d)." % (dataset['international'],
dataset['number']))
print('')
print("[get_symmetry_dataset] ['pointgroup']")
print(" Pointgroup of Rutile is %s." % (dataset['pointgroup']))
print('')
print("[get_symmetry_dataset] ['hall']")
print(" Hall symbol of Rutile is %s (%d)." % (dataset['hall'],
dataset['hall_number']))
print('')
print("[get_symmetry_dataset] ['wyckoffs']")
alphabet = "abcdefghijklmnopqrstuvwxyz"
print(" Wyckoff letters of Rutile are: ", dataset['wyckoffs'])
print('')
print("[get_symmetry_dataset] ['equivalent_atoms']")
print(" Mapping to equivalent atoms of Rutile are: ")
for i, x in enumerate(dataset['equivalent_atoms']):
print(" %d -> %d" % (i + 1, x + 1))
print('')
print("[get_symmetry_dataset] ['rotations'], ['translations']")
print(" Symmetry operations of Rutile unitcell are:")
for i, (rot,trans) in enumerate(zip(dataset['rotations'],
dataset['translations'])):
print(" --------------- %4d ---------------" % (i + 1))
print(" rotation:")
for x in rot:
print(" [%2d %2d %2d]" % (x[0], x[1], x[2]))
print(" translation:")
print(" (%8.5f %8.5f %8.5f)" % (trans[0], trans[1], trans[2]))
print('')
print("[refine_cell]")
print(" Refine distorted rutile structure")
lattice, positions, numbers = spglib.refine_cell(rutile_dist, symprec=1e-1)
show_cell(lattice, positions, numbers)
print('')
print("[find_primitive]")
print(" Fine primitive distorted silicon structure")
lattice, positions, numbers = spglib.find_primitive(silicon_dist, symprec=1e-1)
show_cell(lattice, positions, numbers)
print('')
print("[standardize_cell]")
print(" Standardize distorted rutile structure:")
print(" (to_primitive=0 and no_idealize=0)")
lattice, positions, numbers = spglib.standardize_cell(rutile_dist,
to_primitive=0,
no_idealize=0,
symprec=1e-1)
show_cell(lattice, positions, numbers)
print('')
print("[standardize_cell]")
print(" Standardize distorted rutile structure:")
print(" (to_primitive=0 and no_idealize=1)")
lattice, positions, numbers = spglib.standardize_cell(rutile_dist,
to_primitive=0,
no_idealize=1,
symprec=1e-1)
show_cell(lattice, positions, numbers)
print('')
print("[standardize_cell]")
print(" Standardize distorted silicon structure:")
print(" (to_primitive=1 and no_idealize=0)")
lattice, positions, numbers = spglib.standardize_cell(silicon_dist,
to_primitive=1,
no_idealize=0,
symprec=1e-1)
show_cell(lattice, positions, numbers)
print('')
print("[standardize_cell]")
print(" Standardize distorted silicon structure:")
print(" (to_primitive=1 and no_idealize=1)")
lattice, positions, numbers = spglib.standardize_cell(silicon_dist,
to_primitive=1,
no_idealize=1,
symprec=1e-1)
show_cell(lattice, positions, numbers)
print('')
symmetry = spglib.get_symmetry(silicon)
print("[get_symmetry]")
print(" Number of symmetry operations of silicon conventional")
print(" unit cell is %d (192)." % len(symmetry['rotations']))
show_symmetry(symmetry)
print('')
symmetry = spglib.get_symmetry_from_database(525)
print("[get_symmetry_from_database]")
print(" Number of symmetry operations of silicon conventional")
print(" unit cell is %d (192)." % len(symmetry['rotations']))
show_symmetry(symmetry)
print('')
reduced_lattice = spglib.niggli_reduce(niggli_lattice)
print("[niggli_reduce]")
print(" Original lattice")
show_lattice(niggli_lattice)
print(" Reduced lattice")
show_lattice(reduced_lattice)
print('')
mapping, grid = spglib.get_ir_reciprocal_mesh([11, 11, 11],
silicon_prim,
is_shift=[0, 0, 0])
num_ir_kpt = len(np.unique(mapping))
print("[get_ir_reciprocal_mesh]")
print(" Number of irreducible k-points of primitive silicon with")
print(" 11x11x11 Monkhorst-Pack mesh is %d (56)." % num_ir_kpt)
print('')
mapping, grid = spglib.get_ir_reciprocal_mesh([8, 8, 8],
rutile,
is_shift=[1, 1, 1])
num_ir_kpt = len(np.unique(mapping))
print("[get_ir_reciprocal_mesh]")
print(" Number of irreducible k-points of Rutile with")
print(" 8x8x8 Monkhorst-Pack mesh is %d (40)." % num_ir_kpt)
print('')
mapping, grid = spglib.get_ir_reciprocal_mesh([9, 9, 8],
MgB2,
is_shift=[0, 0, 1])
num_ir_kpt = len(np.unique(mapping))
print("[get_ir_reciprocal_mesh]")
print(" Number of irreducible k-points of MgB2 with")
print(" 9x9x8 Monkhorst-Pack mesh is %s (48)." % num_ir_kpt)
print('')
[get_spacegroup]
Spacegroup of Silicon is Fd-3m (227).
[get_spacegroup]
Spacegroup of Silicon (ASE Atoms-like format) is Fd-3m (227).
[get_spacegroup]
Spacegroup of Rutile is P4_2/mnm (136).
[get_spacegroup]
Spacegroup of MgB2 is P6/mmm (191).
[get_symmetry]
Symmetry operations of Rutile unitcell are:
--------------- 1 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 2 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 3 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 4 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 5 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 6 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 7 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 8 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 9 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 10 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 11 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 12 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 13 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 14 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 15 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 16 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
[get_symmetry]
Symmetry operations of MgB2 are:
--------------- 1 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 2 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 3 ---------------
rotation:
[ 1 -1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 4 ---------------
rotation:
[-1 1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 5 ---------------
rotation:
[ 0 -1 0]
[ 1 -1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 6 ---------------
rotation:
[ 0 1 0]
[-1 1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 7 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 8 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 9 ---------------
rotation:
[-1 1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 10 ---------------
rotation:
[ 1 -1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 11 ---------------
rotation:
[ 0 1 0]
[-1 1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 12 ---------------
rotation:
[ 0 -1 0]
[ 1 -1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 13 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 14 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 15 ---------------
rotation:
[-1 0 0]
[-1 1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 16 ---------------
rotation:
[ 1 0 0]
[ 1 -1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 17 ---------------
rotation:
[-1 1 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 18 ---------------
rotation:
[ 1 -1 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 19 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 20 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 21 ---------------
rotation:
[ 1 0 0]
[ 1 -1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 22 ---------------
rotation:
[-1 0 0]
[-1 1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 23 ---------------
rotation:
[ 1 -1 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 24 ---------------
rotation:
[-1 1 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
[get_pointgroup]
Pointgroup of Rutile is 6/mmm.
[get_symmetry_dataset] ['international']
Spacegroup of Rutile is P4_2/mnm (136).
[get_symmetry_dataset] ['pointgroup']
Pointgroup of Rutile is 4/mmm.
[get_symmetry_dataset] ['hall']
Hall symbol of Rutile is -P 4n 2n (419).
[get_symmetry_dataset] ['wyckoffs']
Wyckoff letters of Rutile are: ['a', 'a', 'f', 'f', 'f', 'f']
[get_symmetry_dataset] ['equivalent_atoms']
Mapping to equivalent atoms of Rutile are:
1 -> 1
2 -> 1
3 -> 3
4 -> 3
5 -> 3
6 -> 3
[get_symmetry_dataset] ['rotations'], ['translations']
Symmetry operations of Rutile unitcell are:
--------------- 1 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 2 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 3 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 4 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 5 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 6 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 7 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 8 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 9 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 10 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 11 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 12 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 13 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 14 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.50000)
--------------- 15 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 16 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
[refine_cell]
Refine distorted rutile structure
Basis vectors:
a 4.00000 0.00000 0.00000
b 0.00000 4.00000 0.00000
c 0.00000 0.00000 3.00000
Atomic points:
14 0.00000 0.00000 0.00000
14 0.50000 0.50000 0.50000
8 0.29995 0.29995 0.00000
8 0.70005 0.70005 0.00000
8 0.20005 0.79995 0.50000
8 0.79995 0.20005 0.50000
[find_primitive]
Fine primitive distorted silicon structure
Basis vectors:
a 0.00000 2.00000 2.00000
b 2.00000 0.00000 2.00000
c 2.00000 2.00000 0.00000
Atomic points:
14 0.25000 0.25000 0.25000
14 0.00000 0.00000 0.00000
[standardize_cell]
Standardize distorted rutile structure:
(to_primitive=0 and no_idealize=0)
Basis vectors:
a 4.00000 0.00000 0.00000
b 0.00000 4.00000 0.00000
c 0.00000 0.00000 3.00000
Atomic points:
14 0.00000 0.00000 0.00000
14 0.50000 0.50000 0.50000
8 0.29995 0.29995 0.00000
8 0.70005 0.70005 0.00000
8 0.20005 0.79995 0.50000
8 0.79995 0.20005 0.50000
[standardize_cell]
Standardize distorted rutile structure:
(to_primitive=0 and no_idealize=1)
Basis vectors:
a 3.97000 0.00000 0.00000
b 0.00000 4.03000 0.00000
c 0.00000 0.00000 3.00000
Atomic points:
14 0.00000 0.00000 0.00000
14 0.50010 0.50000 0.50000
8 0.30000 0.30000 0.00000
8 0.70000 0.70000 0.00200
8 0.20000 0.80000 0.50000
8 0.80000 0.20000 0.50000
[standardize_cell]
Standardize distorted silicon structure:
(to_primitive=1 and no_idealize=0)
Basis vectors:
a 0.00000 2.00000 2.00000
b 2.00000 0.00000 2.00000
c 2.00000 2.00000 0.00000
Atomic points:
14 0.25000 0.25000 0.25000
14 0.00000 0.00000 0.00000
[standardize_cell]
Standardize distorted silicon structure:
(to_primitive=1 and no_idealize=1)
Basis vectors:
a 0.00000 2.00000 -1.99500
b 2.00500 2.00000 0.00000
c 2.00500 0.00000 -1.99500
Atomic points:
14 0.99975 0.00025 0.00025
14 0.74975 0.75025 0.74975
[get_symmetry]
Number of symmetry operations of silicon conventional
unit cell is 192 (192).
--------------- 1 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 2 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 3 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 4 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 5 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 6 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 7 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 8 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 9 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 10 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 11 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 12 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 13 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 14 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 15 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 16 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 17 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 18 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 19 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 20 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 21 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 22 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 23 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 24 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 25 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 26 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 27 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 28 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 29 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 30 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 31 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 32 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 33 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 34 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 35 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 36 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 37 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 38 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 39 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 40 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 41 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 42 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 43 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 44 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 45 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 46 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 47 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 48 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 49 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 50 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 51 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 52 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 53 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 54 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 55 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 56 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 57 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 58 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 59 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 60 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 61 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 62 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 63 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 64 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 65 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 66 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 67 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 68 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 69 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 70 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 71 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 72 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 73 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 74 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 75 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 76 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 77 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 78 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 79 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 80 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 81 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 82 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 83 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 84 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 85 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 86 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 87 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 88 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 89 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 90 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 91 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 92 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 93 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 94 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 95 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 96 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 97 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 98 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 99 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 100 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 101 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 102 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 103 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 104 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 105 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 106 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 107 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 108 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 109 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 110 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 111 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 112 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 113 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 114 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 115 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 116 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 117 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 118 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 119 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 120 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 121 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 122 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 123 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 124 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 125 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 126 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 127 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 128 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 129 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 130 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 131 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 132 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 133 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 134 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 135 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 136 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 137 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 138 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 139 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 140 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 141 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 142 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 143 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 144 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 145 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 146 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 147 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 148 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 149 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 150 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 151 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 152 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 153 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 154 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 155 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 156 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 157 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 158 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 159 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 160 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 161 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 162 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 163 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 164 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 165 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 166 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 167 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 168 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 169 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 170 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 171 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 172 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 173 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 174 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 175 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 176 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 177 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 178 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 179 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 180 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 181 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 182 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 183 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 184 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 185 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 186 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 187 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 188 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 189 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 190 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 191 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 192 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.50000 0.00000 0.50000)
[get_symmetry_from_database]
Number of symmetry operations of silicon conventional
unit cell is 192 (192).
--------------- 1 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 2 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 3 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 4 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 5 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 6 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 7 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 8 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 9 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 10 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 11 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 12 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 13 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 14 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 15 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 16 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 17 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 18 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 19 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 20 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 21 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 22 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 23 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 24 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 25 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 26 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 27 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 28 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 29 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 30 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 31 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 32 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 33 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 34 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 35 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 36 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 37 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 38 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 39 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 40 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 41 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 42 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 43 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 44 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 45 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 46 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 47 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 48 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 49 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 50 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 51 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 52 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 53 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 54 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 55 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 56 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 57 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 58 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 59 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 60 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 61 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 62 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 63 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 64 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 65 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 66 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 67 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 68 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 69 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 70 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 71 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 72 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 73 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 74 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 75 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 76 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 77 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 78 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 79 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 80 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 81 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 82 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 83 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 84 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 85 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 86 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 87 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 88 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 89 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 90 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 91 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 92 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 93 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 94 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 95 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 96 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 97 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 98 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 99 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 100 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 101 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 102 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 103 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 104 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 105 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 106 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 107 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 108 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 109 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 110 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 111 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 112 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 113 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 114 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 115 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 116 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 117 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 118 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 119 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 120 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 121 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 122 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 123 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 124 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 125 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 126 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 127 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 128 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 129 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 130 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 131 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 132 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 133 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 134 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 135 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 136 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 137 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 138 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 139 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 140 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 141 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 142 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 143 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 144 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 145 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 146 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 147 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 148 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.25000 0.75000 0.75000)
--------------- 149 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 150 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 151 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 152 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.25000 0.25000 0.25000)
--------------- 153 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 154 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 155 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 156 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 157 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 158 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 159 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 160 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 161 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 162 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 163 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 164 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.75000 0.25000 0.75000)
--------------- 165 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 166 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 167 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 168 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 169 ---------------
rotation:
[-1 0 0]
[ 0 -1 0]
[ 0 0 -1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 170 ---------------
rotation:
[ 0 1 0]
[-1 0 0]
[ 0 0 -1]
translation:
( 0.50000 0.50000 0.00000)
--------------- 171 ---------------
rotation:
[ 1 0 0]
[ 0 1 0]
[ 0 0 -1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 172 ---------------
rotation:
[ 0 -1 0]
[ 1 0 0]
[ 0 0 -1]
translation:
( 0.00000 0.50000 0.50000)
--------------- 173 ---------------
rotation:
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
translation:
( 0.75000 0.75000 0.25000)
--------------- 174 ---------------
rotation:
[ 0 1 0]
[ 1 0 0]
[ 0 0 1]
translation:
( 0.50000 0.00000 0.50000)
--------------- 175 ---------------
rotation:
[ 1 0 0]
[ 0 -1 0]
[ 0 0 1]
translation:
( 0.75000 0.25000 0.75000)
--------------- 176 ---------------
rotation:
[ 0 -1 0]
[-1 0 0]
[ 0 0 1]
translation:
( 0.00000 0.00000 0.00000)
--------------- 177 ---------------
rotation:
[ 0 0 -1]
[-1 0 0]
[ 0 -1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 178 ---------------
rotation:
[ 0 0 -1]
[ 0 1 0]
[-1 0 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 179 ---------------
rotation:
[ 0 0 -1]
[ 1 0 0]
[ 0 1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 180 ---------------
rotation:
[ 0 0 -1]
[ 0 -1 0]
[ 1 0 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 181 ---------------
rotation:
[ 0 0 1]
[-1 0 0]
[ 0 1 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 182 ---------------
rotation:
[ 0 0 1]
[ 0 1 0]
[ 1 0 0]
translation:
( 0.00000 0.50000 0.50000)
--------------- 183 ---------------
rotation:
[ 0 0 1]
[ 1 0 0]
[ 0 -1 0]
translation:
( 0.25000 0.75000 0.75000)
--------------- 184 ---------------
rotation:
[ 0 0 1]
[ 0 -1 0]
[-1 0 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 185 ---------------
rotation:
[ 0 -1 0]
[ 0 0 -1]
[-1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 186 ---------------
rotation:
[-1 0 0]
[ 0 0 -1]
[ 0 1 0]
translation:
( 0.50000 0.50000 0.00000)
--------------- 187 ---------------
rotation:
[ 0 1 0]
[ 0 0 -1]
[ 1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 188 ---------------
rotation:
[ 1 0 0]
[ 0 0 -1]
[ 0 -1 0]
translation:
( 0.50000 0.00000 0.50000)
--------------- 189 ---------------
rotation:
[ 0 1 0]
[ 0 0 1]
[-1 0 0]
translation:
( 0.75000 0.75000 0.25000)
--------------- 190 ---------------
rotation:
[ 1 0 0]
[ 0 0 1]
[ 0 1 0]
translation:
( 0.00000 0.00000 0.00000)
--------------- 191 ---------------
rotation:
[ 0 -1 0]
[ 0 0 1]
[ 1 0 0]
translation:
( 0.25000 0.25000 0.25000)
--------------- 192 ---------------
rotation:
[-1 0 0]
[ 0 0 1]
[ 0 -1 0]
translation:
( 0.00000 0.50000 0.50000)
[niggli_reduce]
Original lattice
Basis vectors:
a 3.00000 0.00000 0.00000
b -3.66667 3.68179 0.00000
c -0.66667 -1.34295 1.32365
Reduced lattice
Basis vectors:
a -0.66667 -1.34295 1.32365
b 2.33333 -1.34295 1.32365
c 1.00000 0.99589 2.64730
[get_ir_reciprocal_mesh]
Number of irreducible k-points of primitive silicon with
11x11x11 Monkhorst-Pack mesh is 56 (56).
[get_ir_reciprocal_mesh]
Number of irreducible k-points of Rutile with
8x8x8 Monkhorst-Pack mesh is 40 (40).
[get_ir_reciprocal_mesh]
Number of irreducible k-points of MgB2 with
9x9x8 Monkhorst-Pack mesh is 48 (48).