cantellated heptacross
- general polytopal classes:
- Wythoffian polyexa
links
| Acronym | sarz |
| Name |
small rhombated hecatonicosoctaexon, cantellated heptacross |
| Circumradius | sqrt(3) = 1.732051 |
| Coordinates | (2/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0, 0, 0) & all permutations, all changes of sign |
| Face vector | 840, 7560, 19320, 24080, 15456, 4200, 226 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3o3x3o3o3o4o . . . . . . . | 840 | 2 16 | 1 16 8 48 | 8 48 24 64 | 24 64 32 32 | 32 32 16 2 | 16 2 1 --------------+-----+----------+---------------------+---------------------+--------------------+------------------+---------- x . . . . . . | 2 | 840 * | 1 8 0 0 | 8 24 0 0 | 24 32 0 0 | 32 16 0 0 | 16 1 0 . . x . . . . | 2 | * 6720 | 0 1 1 6 | 1 6 6 12 | 6 12 12 8 | 12 8 8 1 | 8 1 1 --------------+-----+----------+---------------------+---------------------+--------------------+------------------+---------- x3o . . . . . | 3 | 3 0 | 280 * * * ♦ 8 0 0 0 | 24 0 0 0 | 32 0 0 0 | 16 0 0 x . x . . . . | 4 | 2 2 | * 3360 * * | 1 6 0 0 | 6 12 0 0 | 12 8 0 0 | 8 1 0 . o3x . . . . | 3 | 0 3 | * * 2240 * | 1 0 6 0 | 6 0 12 0 | 12 0 8 0 | 8 0 1 . . x3o . . . | 3 | 0 3 | * * * 13440 | 0 1 1 4 | 1 4 4 4 | 4 4 4 1 | 4 1 1 --------------+-----+----------+---------------------+---------------------+--------------------+------------------+---------- x3o3x . . . . ♦ 12 | 12 12 | 4 6 4 0 | 560 * * * ♦ 6 0 0 0 | 12 0 0 0 | 8 0 0 x . x3o . . . ♦ 6 | 3 6 | 0 3 0 2 | * 6720 * * | 1 4 0 0 | 4 4 0 0 | 4 1 0 . o3x3o . . . ♦ 6 | 0 12 | 0 0 4 4 | * * 3360 * | 1 0 4 0 | 4 0 4 0 | 4 0 1 . . x3o3o . . ♦ 4 | 0 6 | 0 0 0 4 | * * * 13440 | 0 1 1 2 | 1 2 2 1 | 2 1 1 --------------+-----+----------+---------------------+---------------------+--------------------+------------------+---------- x3o3x3o . . . ♦ 30 | 30 60 | 10 30 20 20 | 5 10 5 0 | 672 * * * | 4 0 0 0 | 4 0 0 x . x3o3o . . ♦ 8 | 4 12 | 0 6 0 8 | 0 4 0 2 | * 6720 * * | 1 2 0 0 | 2 1 0 . o3x3o3o . . ♦ 10 | 0 30 | 0 0 10 20 | 0 0 5 5 | * * 2688 * | 1 0 2 0 | 2 0 1 . . x3o3o3o . ♦ 5 | 0 10 | 0 0 0 10 | 0 0 0 5 | * * * 5376 | 0 1 1 1 | 1 1 1 --------------+-----+----------+---------------------+---------------------+--------------------+------------------+---------- x3o3x3o3o . . ♦ 60 | 60 180 | 20 90 60 120 | 15 60 30 30 | 6 15 6 0 | 448 * * * | 2 0 0 x . x3o3o3o . ♦ 10 | 5 20 | 0 10 0 20 | 0 10 0 10 | 0 5 0 2 | * 2688 * * | 1 1 0 . o3x3o3o3o . ♦ 15 | 0 60 | 0 0 20 60 | 0 0 15 30 | 0 0 6 6 | * * 896 * | 1 0 1 . . x3o3o3o4o ♦ 10 | 0 40 | 0 0 0 80 | 0 0 0 80 | 0 0 0 32 | * * * 168 | 0 1 1 --------------+-----+----------+---------------------+---------------------+--------------------+------------------+---------- x3o3x3o3o3o . ♦ 105 | 105 420 | 35 210 140 420 | 35 210 105 210 | 21 105 42 42 | 7 21 7 0 | 128 * * x . x3o3o3o4o ♦ 20 | 10 80 | 0 40 0 160 | 0 80 0 160 | 0 80 0 64 | 0 32 0 2 | * 84 * . o3x3o3o3o4o ♦ 60 | 0 480 | 0 0 160 960 | 0 0 240 960 | 0 0 192 384 | 0 0 64 12 | * * 14
x3o3x3o3o3o4/3o . . . . . . . | 840 | 2 16 | 1 16 8 48 | 8 48 24 64 | 24 64 32 32 | 32 32 16 2 | 16 2 1 ----------------+-----+----------+---------------------+---------------------+--------------------+------------------+---------- x . . . . . . | 2 | 840 * | 1 8 0 0 | 8 24 0 0 | 24 32 0 0 | 32 16 0 0 | 16 1 0 . . x . . . . | 2 | * 6720 | 0 1 1 6 | 1 6 6 12 | 6 12 12 8 | 12 8 8 1 | 8 1 1 ----------------+-----+----------+---------------------+---------------------+--------------------+------------------+---------- x3o . . . . . | 3 | 3 0 | 280 * * * ♦ 8 0 0 0 | 24 0 0 0 | 32 0 0 0 | 16 0 0 x . x . . . . | 4 | 2 2 | * 3360 * * | 1 6 0 0 | 6 12 0 0 | 12 8 0 0 | 8 1 0 . o3x . . . . | 3 | 0 3 | * * 2240 * | 1 0 6 0 | 6 0 12 0 | 12 0 8 0 | 8 0 1 . . x3o . . . | 3 | 0 3 | * * * 13440 | 0 1 1 4 | 1 4 4 4 | 4 4 4 1 | 4 1 1 ----------------+-----+----------+---------------------+---------------------+--------------------+------------------+---------- x3o3x . . . . ♦ 12 | 12 12 | 4 6 4 0 | 560 * * * ♦ 6 0 0 0 | 12 0 0 0 | 8 0 0 x . x3o . . . ♦ 6 | 3 6 | 0 3 0 2 | * 6720 * * | 1 4 0 0 | 4 4 0 0 | 4 1 0 . o3x3o . . . ♦ 6 | 0 12 | 0 0 4 4 | * * 3360 * | 1 0 4 0 | 4 0 4 0 | 4 0 1 . . x3o3o . . ♦ 4 | 0 6 | 0 0 0 4 | * * * 13440 | 0 1 1 2 | 1 2 2 1 | 2 1 1 ----------------+-----+----------+---------------------+---------------------+--------------------+------------------+---------- x3o3x3o . . . ♦ 30 | 30 60 | 10 30 20 20 | 5 10 5 0 | 672 * * * | 4 0 0 0 | 4 0 0 x . x3o3o . . ♦ 8 | 4 12 | 0 6 0 8 | 0 4 0 2 | * 6720 * * | 1 2 0 0 | 2 1 0 . o3x3o3o . . ♦ 10 | 0 30 | 0 0 10 20 | 0 0 5 5 | * * 2688 * | 1 0 2 0 | 2 0 1 . . x3o3o3o . ♦ 5 | 0 10 | 0 0 0 10 | 0 0 0 5 | * * * 5376 | 0 1 1 1 | 1 1 1 ----------------+-----+----------+---------------------+---------------------+--------------------+------------------+---------- x3o3x3o3o . . ♦ 60 | 60 180 | 20 90 60 120 | 15 60 30 30 | 6 15 6 0 | 448 * * * | 2 0 0 x . x3o3o3o . ♦ 10 | 5 20 | 0 10 0 20 | 0 10 0 10 | 0 5 0 2 | * 2688 * * | 1 1 0 . o3x3o3o3o . ♦ 15 | 0 60 | 0 0 20 60 | 0 0 15 30 | 0 0 6 6 | * * 896 * | 1 0 1 . . x3o3o3o4/3o ♦ 10 | 0 40 | 0 0 0 80 | 0 0 0 80 | 0 0 0 32 | * * * 168 | 0 1 1 ----------------+-----+----------+---------------------+---------------------+--------------------+------------------+---------- x3o3x3o3o3o . ♦ 105 | 105 420 | 35 210 140 420 | 35 210 105 210 | 21 105 42 42 | 7 21 7 0 | 128 * * x . x3o3o3o4/3o ♦ 20 | 10 80 | 0 40 0 160 | 0 80 0 160 | 0 80 0 64 | 0 32 0 2 | * 84 * . o3x3o3o3o4/3o ♦ 60 | 0 480 | 0 0 160 960 | 0 0 240 960 | 0 0 192 384 | 0 0 64 12 | * * 14
o3o3o *b3o3x3o3x . . . . . . . | 840 | 16 2 | 48 8 16 1 | 64 24 48 8 | 16 16 32 64 24 | 2 8 16 8 16 32 | 1 2 8 8 -----------------+-----+----------+---------------------+---------------------+-------------------------+---------------------------+------------ . . . . x . . | 2 | 6720 * | 6 1 1 0 | 12 6 6 1 | 4 4 12 12 6 | 1 4 4 4 4 12 | 1 1 4 4 . . . . . . x | 2 | * 840 | 0 0 8 1 | 0 0 24 8 | 0 0 0 32 24 | 0 0 8 0 8 32 | 0 1 8 8 -----------------+-----+----------+---------------------+---------------------+-------------------------+---------------------------+------------ . . . o3x . . | 3 | 3 0 | 13440 * * * | 4 1 1 0 | 2 2 4 4 1 | 1 2 2 2 2 4 | 1 1 2 2 . . . . x3o . | 3 | 3 0 | * 2240 * * | 0 6 0 1 | 0 0 12 0 6 | 0 4 0 4 0 12 | 1 0 4 4 . . . . x . x | 4 | 2 2 | * * 3360 * | 0 0 6 1 | 0 0 0 12 6 | 0 0 4 0 4 12 | 0 1 4 4 . . . . . o3x | 3 | 0 3 | * * * 280 ♦ 0 0 0 8 | 0 0 0 0 24 | 0 0 0 0 0 32 | 0 0 8 8 -----------------+-----+----------+---------------------+---------------------+-------------------------+---------------------------+------------ . o . *b3o3x . . ♦ 4 | 6 0 | 4 0 0 0 | 13440 * * * | 1 1 1 1 0 | 1 1 1 1 1 1 | 1 1 1 1 . . . o3x3o . ♦ 6 | 12 0 | 4 4 0 0 | * 3360 * * | 0 0 4 0 1 | 0 2 0 2 0 4 | 1 0 2 2 . . . o3x . x ♦ 6 | 6 3 | 2 0 3 0 | * * 6720 * | 0 0 0 4 1 | 0 0 2 0 2 4 | 0 1 2 2 . . . . x3o3x ♦ 12 | 12 12 | 0 4 6 4 | * * * 560 ♦ 0 0 0 0 6 | 0 0 0 0 0 12 | 0 0 4 4 -----------------+-----+----------+---------------------+---------------------+-------------------------+---------------------------+------------ o3o . *b3o3x . . ♦ 5 | 10 0 | 10 0 0 0 | 5 0 0 0 | 2688 * * * * | 1 1 1 0 0 0 | 1 1 1 0 . o3o *b3o3x . . ♦ 5 | 10 0 | 10 0 0 0 | 5 0 0 0 | * 2688 * * * | 1 0 0 1 1 0 | 1 1 0 1 . o . *b3o3x3o . ♦ 10 | 30 0 | 20 10 0 0 | 5 5 0 0 | * * 2688 * * | 0 1 0 1 0 1 | 1 0 1 1 . o . *b3o3x . x ♦ 8 | 12 4 | 8 0 6 0 | 2 0 4 0 | * * * 6720 * | 0 0 1 0 1 1 | 0 1 1 1 . . . o3x3o3x ♦ 30 | 60 30 | 20 20 30 10 | 0 5 10 5 | * * * * 672 | 0 0 0 0 0 4 | 0 0 2 2 -----------------+-----+----------+---------------------+---------------------+-------------------------+---------------------------+------------ o3o3o *b3o3x . . ♦ 10 | 40 0 | 80 0 0 0 | 80 0 0 0 | 16 16 0 0 0 | 168 * * * * * | 1 1 0 0 o3o . *b3o3x3o . ♦ 15 | 60 0 | 60 20 0 0 | 30 15 0 0 | 6 0 6 0 0 | * 448 * * * * | 1 0 1 0 o3o . *b3o3x . x ♦ 10 | 20 5 | 20 0 10 0 | 10 0 10 0 | 2 0 0 5 0 | * * 1344 * * * | 0 1 1 0 . o3o *b3o3x3o . ♦ 15 | 60 0 | 60 20 0 0 | 30 15 0 0 | 0 6 6 0 0 | * * * 448 * * | 1 0 0 1 . o3o *b3o3x . x ♦ 10 | 20 5 | 20 0 10 0 | 10 0 10 0 | 0 2 0 5 0 | * * * * 1344 * | 0 1 0 1 . o . *b3o3x3o3x ♦ 60 | 180 60 | 120 60 90 20 | 30 30 60 15 | 0 0 6 15 6 | * * * * * 448 | 0 0 1 1 -----------------+-----+----------+---------------------+---------------------+-------------------------+---------------------------+------------ o3o3o *b3o3x3o . ♦ 60 | 480 0 | 960 160 0 0 | 960 240 0 0 | 192 192 192 0 0 | 12 32 0 32 0 0 | 14 * * * o3o3o *b3o3x . x ♦ 20 | 80 10 | 160 0 40 0 | 160 0 80 0 | 32 32 0 80 0 | 2 0 16 0 16 0 | * 84 * * o3o . *b3o3x3o3x ♦ 105 | 420 105 | 420 140 210 35 | 210 105 210 35 | 42 0 42 105 21 | 0 7 21 0 0 7 | * * 64 * . o3o *b3o3x3o3x ♦ 105 | 420 105 | 420 140 210 35 | 210 105 210 35 | 0 42 42 105 21 | 0 0 0 7 21 7 | * * * 64
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