bistericated octaexon
- general polytopal classes:
- Wythoffian polyexa
links
| Acronym | sabach |
| Name |
small bicellated hexadecaexon, bistericated octaexon |
| Circumradius | sqrt(2) = 1.414214 |
| Face vector | 420, 3360, 9520, 12600, 7952, 2128, 198 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
o3x3o3o3o3x3o . . . . . . . | 420 | 8 8 | 4 12 48 12 4 | 6 24 8 48 48 24 8 6 | 4 24 24 12 2 16 24 24 16 24 2 4 | 1 8 12 12 8 12 4 8 12 8 1 | 2 4 6 4 2 --------------+-----+-----------+------------------------+-------------------------------------+----------------------------------------------------+------------------------------------------+------------- . x . . . . . | 2 | 1680 * | 1 3 6 0 0 | 3 3 6 12 6 3 0 0 | 3 12 6 3 1 6 6 6 2 3 0 0 | 1 6 6 6 2 3 2 3 3 1 0 | 2 3 3 1 1 . . . . . x . | 2 | * 1680 | 0 0 6 3 1 | 0 3 0 6 12 6 3 3 | 0 3 6 3 0 2 6 6 6 12 1 3 | 0 1 3 3 3 6 2 2 6 6 1 | 1 1 3 3 2 --------------+-----+-----------+------------------------+-------------------------------------+----------------------------------------------------+------------------------------------------+------------- o3x . . . . . | 3 | 3 0 | 560 * * * * | 3 6 0 0 0 0 0 0 | 3 12 6 3 0 0 0 0 0 0 0 0 | 1 6 6 6 2 3 0 0 0 0 0 | 2 3 3 1 0 . x3o . . . . | 3 | 3 0 | * 1680 * * * | 1 0 2 4 0 0 0 0 | 2 4 0 0 1 4 2 2 0 0 0 0 | 1 4 2 2 0 0 2 2 1 0 0 | 2 2 1 0 1 . x . . . x . | 4 | 2 2 | * * 5040 * * | 0 1 0 2 2 1 0 0 | 0 2 2 1 0 1 2 2 1 2 0 0 | 0 1 2 2 1 2 1 1 2 1 0 | 1 1 2 1 1 . . . . o3x . | 3 | 0 3 | * * * 1680 * | 0 0 0 0 4 0 2 1 | 0 0 2 0 0 0 2 0 4 4 1 2 | 0 0 1 0 2 2 2 0 2 4 1 | 1 0 1 2 2 . . . . . x3o | 3 | 0 3 | * * * * 560 | 0 0 0 0 0 6 0 3 | 0 0 0 3 0 0 0 6 0 12 0 3 | 0 0 0 3 0 6 0 2 6 6 1 | 0 1 3 3 2 --------------+-----+-----------+------------------------+-------------------------------------+----------------------------------------------------+------------------------------------------+------------- o3x3o . . . . ♦ 6 | 12 0 | 4 4 0 0 0 | 420 * * * * * * * | 2 4 0 0 0 0 0 0 0 0 0 0 | 1 4 2 2 0 0 0 0 0 0 0 | 2 2 1 0 0 o3x . . . x . ♦ 6 | 6 3 | 2 0 3 0 0 | * 1680 * * * * * * | 0 2 2 1 0 0 0 0 0 0 0 0 | 0 1 2 2 1 2 0 0 0 0 0 | 1 1 2 1 0 . x3o3o . . . ♦ 4 | 6 0 | 0 4 0 0 0 | * * 840 * * * * * | 1 0 0 0 1 2 0 0 0 0 0 0 | 1 2 0 0 0 0 2 1 0 0 0 | 2 1 0 0 1 . x3o . . x . ♦ 6 | 6 3 | 0 2 3 0 0 | * * * 3360 * * * * | 0 1 0 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0 0 1 1 1 0 0 | 1 1 1 0 1 . x . . o3x . ♦ 6 | 3 6 | 0 0 3 2 0 | * * * * 3360 * * * | 0 0 1 0 0 0 1 0 1 1 0 0 | 0 0 1 0 1 1 1 0 1 1 0 | 1 0 1 1 1 . x . . . x3o ♦ 6 | 3 6 | 0 0 3 0 2 | * * * * * 1680 * * | 0 0 0 1 0 0 0 2 0 2 0 0 | 0 0 0 2 0 2 0 1 2 1 0 | 0 1 2 1 1 . . . o3o3x . ♦ 4 | 0 6 | 0 0 0 4 0 | * * * * * * 840 * | 0 0 0 0 0 0 0 0 2 0 1 1 | 0 0 0 0 1 0 2 0 0 2 1 | 1 0 0 1 2 . . . . o3x3o ♦ 6 | 0 12 | 0 0 0 4 4 | * * * * * * * 420 | 0 0 0 0 0 0 0 0 0 4 0 2 | 0 0 0 0 0 2 0 0 2 4 1 | 0 0 1 2 2 --------------+-----+-----------+------------------------+-------------------------------------+----------------------------------------------------+------------------------------------------+------------- o3x3o3o . . . ♦ 10 | 30 0 | 10 20 0 0 0 | 5 0 5 0 0 0 0 0 | 168 * * * * * * * * * * * | 1 2 0 0 0 0 0 0 0 0 0 | 2 1 0 0 0 o3x3o . . x . ♦ 12 | 24 6 | 8 8 12 0 0 | 2 4 0 4 0 0 0 0 | * 840 * * * * * * * * * * | 0 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 o3x . . o3x . ♦ 9 | 9 9 | 3 0 9 3 0 | 0 3 0 0 3 0 0 0 | * * 1120 * * * * * * * * * | 0 0 1 0 1 1 0 0 0 0 0 | 1 0 1 1 0 o3x . . . x3o ♦ 9 | 9 9 | 3 0 9 0 3 | 0 3 0 0 0 3 0 0 | * * * 560 * * * * * * * * | 0 0 0 2 0 2 0 0 0 0 0 | 0 1 2 1 0 . x3o3o3o . . ♦ 5 | 10 0 | 0 10 0 0 0 | 0 0 5 0 0 0 0 0 | * * * * 168 * * * * * * * | 1 0 0 0 0 0 2 0 0 0 0 | 2 0 0 0 1 . x3o3o . x . ♦ 8 | 12 4 | 0 8 6 0 0 | 0 0 2 4 0 0 0 0 | * * * * * 840 * * * * * * | 0 1 0 0 0 0 1 1 0 0 0 | 1 1 0 0 1 . x3o . o3x . ♦ 9 | 9 9 | 0 3 9 3 0 | 0 0 0 3 3 0 0 0 | * * * * * * 1120 * * * * * | 0 0 1 0 0 0 1 0 1 0 0 | 1 0 1 0 1 . x3o . . x3o ♦ 9 | 9 9 | 0 3 9 0 3 | 0 0 0 3 0 3 0 0 | * * * * * * * 1120 * * * * | 0 0 0 1 0 0 0 1 1 0 0 | 0 1 1 0 1 . x . o3o3x . ♦ 8 | 4 12 | 0 0 6 8 0 | 0 0 0 0 4 0 2 0 | * * * * * * * * 840 * * * | 0 0 0 0 1 0 1 0 0 1 0 | 1 0 0 1 1 . x . . o3x3o ♦ 12 | 6 24 | 0 0 12 8 8 | 0 0 0 0 4 4 0 2 | * * * * * * * * * 840 * * | 0 0 0 0 0 1 0 0 1 1 0 | 0 0 1 1 1 . . o3o3o3x . ♦ 5 | 0 10 | 0 0 0 10 0 | 0 0 0 0 0 0 5 0 | * * * * * * * * * * 168 * | 0 0 0 0 0 0 2 0 0 0 1 | 1 0 0 0 2 . . . o3o3x3o ♦ 10 | 0 30 | 0 0 0 20 10 | 0 0 0 0 0 0 5 5 | * * * * * * * * * * * 168 | 0 0 0 0 0 0 0 0 0 2 1 | 0 0 0 1 2 --------------+-----+-----------+------------------------+-------------------------------------+----------------------------------------------------+------------------------------------------+------------- o3x3o3o3o . . ♦ 15 | 60 0 | 20 60 0 0 0 | 15 0 30 0 0 0 0 0 | 6 0 0 0 6 0 0 0 0 0 0 0 | 28 * * * * * * * * * * | 2 0 0 0 0 o3x3o3o . x . ♦ 20 | 60 10 | 20 40 30 0 0 | 10 10 10 20 0 0 0 0 | 2 5 0 0 0 5 0 0 0 0 0 0 | * 168 * * * * * * * * * | 1 1 0 0 0 o3x3o . o3x . ♦ 18 | 36 18 | 12 12 36 6 0 | 3 12 0 12 12 0 0 0 | 0 3 4 0 0 0 4 0 0 0 0 0 | * * 280 * * * * * * * * | 1 0 1 0 0 o3x3o . . x3o ♦ 18 | 36 18 | 12 12 36 0 6 | 3 12 0 12 0 12 0 0 | 0 3 0 4 0 0 0 4 0 0 0 0 | * * * 280 * * * * * * * | 0 1 1 0 0 o3x . o3o3x . ♦ 12 | 12 18 | 4 0 18 12 0 | 0 6 0 0 12 0 3 0 | 0 0 4 0 0 0 0 0 3 0 0 0 | * * * * 280 * * * * * * | 1 0 0 1 0 o3x . . o3x3o ♦ 18 | 18 36 | 6 0 36 12 12 | 0 12 0 0 12 12 0 3 | 0 0 4 4 0 0 0 0 0 3 0 0 | * * * * * 280 * * * * * | 0 0 1 1 0 . x3o3o3o3x . ♦ 30 | 60 60 | 0 60 90 60 0 | 0 0 30 60 60 0 30 0 | 0 0 0 0 6 15 20 0 15 0 6 0 | * * * * * * 56 * * * * | 1 0 0 0 1 . x3o3o . x3o ♦ 12 | 18 12 | 0 12 18 0 4 | 0 0 3 12 0 6 0 0 | 0 0 0 0 0 3 0 4 0 0 0 0 | * * * * * * * 280 * * * | 0 1 0 0 1 . x3o . o3x3o ♦ 18 | 18 36 | 0 6 36 12 12 | 0 0 0 12 12 12 0 3 | 0 0 0 0 0 0 4 4 0 3 0 0 | * * * * * * * * 280 * * | 0 0 1 0 1 . x . o3o3x3o ♦ 20 | 10 60 | 0 0 30 40 20 | 0 0 0 0 20 10 10 10 | 0 0 0 0 0 0 0 0 5 5 0 2 | * * * * * * * * * 168 * | 0 0 0 1 1 . . o3o3o3x3o ♦ 15 | 0 60 | 0 0 0 60 20 | 0 0 0 0 0 0 30 15 | 0 0 0 0 0 0 0 0 0 0 6 6 | * * * * * * * * * * 28 | 0 0 0 0 2 --------------+-----+-----------+------------------------+-------------------------------------+----------------------------------------------------+------------------------------------------+------------- o3x3o3o3o3x . ♦ 105 | 420 210 | 140 420 630 210 0 | 105 210 210 420 420 0 105 0 | 42 105 140 0 42 105 140 0 105 0 21 0 | 7 21 35 0 35 0 7 0 0 0 0 | 8 * * * * o3x3o3o . x3o ♦ 30 | 90 30 | 30 60 90 0 10 | 15 30 15 60 0 30 0 0 | 3 15 0 10 0 15 0 20 0 0 0 0 | 0 3 0 5 0 0 0 5 0 0 0 | * 56 * * * o3x3o . o3x3o ♦ 36 | 72 72 | 24 24 144 24 24 | 6 48 0 48 48 48 0 6 | 0 12 16 16 0 0 16 16 0 12 0 0 | 0 0 4 4 0 4 0 0 4 0 0 | * * 70 * * o3x . o3o3x3o ♦ 30 | 30 90 | 10 0 90 60 30 | 0 30 0 0 60 30 15 15 | 0 0 20 10 0 0 0 0 15 15 0 3 | 0 0 0 0 5 5 0 0 0 3 0 | * * * 56 * . x3o3o3o3x3o ♦ 105 | 210 420 | 0 210 630 420 140 | 0 0 105 420 420 210 210 105 | 0 0 0 0 21 105 140 140 105 105 42 42 | 0 0 0 0 0 0 7 35 35 21 7 | * * * * 8
or . . . . . . . | 420 | 16 | 8 24 48 | 12 48 16 96 | 4 48 48 12 4 32 24 | 2 16 24 24 16 4 | 4 8 6 -----------------+-----+------+----------------+--------------------+---------------------------------+-----------------------+---------- . x . . . . . & | 2 | 3360 | 1 3 6 | 3 9 3 18 | 3 15 12 3 1 8 6 | 1 7 9 9 5 2 | 3 4 3 -----------------+-----+------+----------------+--------------------+---------------------------------+-----------------------+---------- o3x . . . . . & | 3 | 3 | 1120 * * | 3 6 0 0 | 3 12 6 3 0 0 0 | 1 6 6 9 2 0 | 2 4 3 . x3o . . . . & | 3 | 3 | * 3360 * | 1 0 2 4 | 2 4 2 0 1 4 2 | 1 4 3 2 2 2 | 3 2 1 . x . . . x . | 4 | 4 | * * 5040 | 0 2 0 4 | 0 4 4 1 0 2 2 | 0 2 4 4 2 1 | 2 2 2 -----------------+-----+------+----------------+--------------------+---------------------------------+-----------------------+---------- o3x3o . . . . & ♦ 6 | 12 | 4 4 0 | 840 * * * | 2 4 0 0 0 0 0 | 1 4 2 2 0 0 | 2 2 1 o3x . . . x . & ♦ 6 | 9 | 2 0 3 | * 3360 * * | 0 2 2 1 0 0 0 | 0 1 2 4 1 0 | 1 2 2 . x3o3o . . . & ♦ 4 | 6 | 0 4 0 | * * 1680 * | 1 0 0 0 1 2 0 | 1 2 0 0 1 2 | 3 1 0 . x3o . . x . & ♦ 6 | 9 | 0 2 3 | * * * 6720 | 0 1 1 0 0 1 1 | 0 1 2 1 1 1 | 2 1 1 -----------------+-----+------+----------------+--------------------+---------------------------------+-----------------------+---------- o3x3o3o . . . & ♦ 10 | 30 | 10 20 0 | 5 0 5 0 | 336 * * * * * * | 1 2 0 0 0 0 | 2 1 0 o3x3o . . x . & ♦ 12 | 30 | 8 8 12 | 2 4 0 4 | * 1680 * * * * * | 0 1 1 1 0 0 | 1 1 1 o3x . . o3x . & ♦ 9 | 18 | 3 3 9 | 0 3 0 3 | * * 2240 * * * * | 0 0 1 1 1 0 | 1 1 1 o3x . . . x3o ♦ 9 | 18 | 6 0 9 | 0 6 0 0 | * * * 560 * * * | 0 0 0 4 0 0 | 0 2 2 . x3o3o3o . . & ♦ 5 | 10 | 0 10 0 | 0 0 5 0 | * * * * 336 * * | 1 0 0 0 0 2 | 3 0 0 . x3o3o . x . & ♦ 8 | 16 | 0 8 6 | 0 0 2 4 | * * * * * 1680 * | 0 1 0 0 1 1 | 2 1 0 . x3o . o3x . ♦ 9 | 18 | 0 6 9 | 0 0 0 6 | * * * * * * 1120 | 0 0 2 0 0 1 | 2 0 1 -----------------+-----+------+----------------+--------------------+---------------------------------+-----------------------+---------- o3x3o3o3o . . & ♦ 15 | 60 | 20 60 0 | 15 0 30 0 | 6 0 0 0 6 0 0 | 56 * * * * * | 2 0 0 o3x3o3o . x . & ♦ 20 | 70 | 20 40 30 | 10 10 10 20 | 2 5 0 0 0 5 0 | * 336 * * * * | 1 1 0 o3x3o . o3x . & ♦ 18 | 54 | 12 18 36 | 3 12 0 24 | 0 3 4 0 0 0 4 | * * 560 * * * | 1 0 1 o3x3o . . x3o & ♦ 18 | 54 | 18 12 36 | 3 24 0 12 | 0 3 4 4 0 0 0 | * * * 560 * * | 0 1 1 o3x . o3o3x . & ♦ 12 | 30 | 4 12 18 | 0 6 3 12 | 0 0 4 0 0 3 0 | * * * * 560 * | 1 1 0 . x3o3o3o3x . ♦ 30 | 120 | 0 120 90 | 0 0 60 120 | 0 0 0 0 12 30 20 | * * * * * 56 | 2 0 0 -----------------+-----+------+----------------+--------------------+---------------------------------+-----------------------+---------- o3x3o3o3o3x . & ♦ 105 | 630 | 140 630 630 | 105 210 315 840 | 42 105 140 0 63 210 140 | 7 21 35 0 35 7 | 16 * * o3x3o3o . x3o & ♦ 30 | 120 | 40 60 90 | 15 60 15 60 | 3 15 20 10 0 15 0 | 0 3 0 5 5 0 | * 112 * o3x3o . o3x3o ♦ 36 | 144 | 48 48 144 | 12 96 0 96 | 0 24 32 16 0 0 16 | 0 0 8 8 0 0 | * * 70
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