-
Notifications
You must be signed in to change notification settings - Fork 0
/
symmetry_cpg.h
389 lines (389 loc) · 67.8 KB
/
symmetry_cpg.h
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
const std::map<std::string, std::vector<Mat<double>>> Symmetry::cpg1 = {
{"C1", { { 1.000000000000000} } },
{"D1", { { 1.000000000000000},
{-1.000000000000000} } },
};
const std::map<std::string, std::vector<Mat<double>>> Symmetry::cpg2 = {
{"C1", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"C2", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"D1", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"D2", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"C4", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000} } },
{"D4", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000} } },
{"C3", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, -0.866025403784440, -0.500000000000000},
{-0.500000000000000, -0.866025403784440, 0.866025403784440, -0.500000000000000} } },
{"D3", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, -0.866025403784440, -0.500000000000000},
{-0.500000000000000, -0.866025403784440, 0.866025403784440, -0.500000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, -0.866025403784440, -0.866025403784440, -0.500000000000000},
{ 0.500000000000000, 0.866025403784440, 0.866025403784440, -0.500000000000000} } },
{"C6", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, 0.866025403784440, -0.866025403784440, 0.500000000000000},
{-0.500000000000000, 0.866025403784440, -0.866025403784440, -0.500000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.866025403784440, -0.500000000000000},
{ 0.500000000000000, -0.866025403784440, 0.866025403784440, 0.500000000000000} } },
{"D6", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, 0.866025403784440, -0.866025403784440, 0.500000000000000},
{-0.500000000000000, 0.866025403784440, -0.866025403784440, -0.500000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.866025403784440, -0.500000000000000},
{ 0.500000000000000, -0.866025403784440, 0.866025403784440, 0.500000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, -0.866025403784440, -0.866025403784440, -0.500000000000000},
{ 0.500000000000000, 0.866025403784440, 0.866025403784440, -0.500000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.866025403784440, 0.500000000000000},
{-0.500000000000000, -0.866025403784440, -0.866025403784440, 0.500000000000000} } },
};
const std::map<std::string, std::vector<Mat<double>>> Symmetry::cpg3 = {
{"C1", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"Ci", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"C2", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"C1h", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"C2h", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"D2", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"C2v", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"D2h", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"C4", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"S4", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"C4h", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"D4", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"C4v", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"D2d", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"D4h", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"C3", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"S6", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"D3", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"C3v", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"D3d", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"C6", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"C3h", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"C6h", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"D6", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"C6v", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"D3h", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"D6h", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, -0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, -0.866025403784440, 0.000000000000000, -0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-0.500000000000000, 0.866025403784440, 0.000000000000000, 0.866025403784440, 0.500000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"T", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000} } },
{"Th", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000} } },
{"O", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000} } },
{"Td", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000} } },
{"Oh", { { 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{-1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000},
{ 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000},
{ 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, 0.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000, -1.000000000000000, 0.000000000000000},
{ 1.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000, 1.000000000000000, 0.000000000000000} } },
};