runcinated heptacross
- general polytopal classes:
- Wythoffian polyexa
links
| Acronym | spaz |
| Name |
small prismated hecatonicosoctaexon, runcinated heptacross |
| Circumradius | sqrt(7/2) = 1.870829 |
| Coordinates | (2/sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0, 0) & all permutations, all changes of sign |
| Face vector | 2240, 23520, 62720, 71120, 38696, 9520, 506 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3o3o3x3o3o4o . . . . . . . | 2240 | 3 18 | 3 36 18 36 | 1 18 18 72 6 36 24 | 6 36 36 48 12 24 3 | 12 24 24 6 8 3 | 8 3 3 1 --------------+------+------------+------------------------+--------------------------------------+-----------------------------------+---------------------------+-------------- x . . . . . . | 2 | 3360 * | 2 12 0 0 | 1 12 6 24 0 0 0 | 6 24 12 16 0 0 0 | 12 16 8 2 0 0 | 8 2 1 0 . . . x . . . | 2 | * 20160 | 0 2 2 4 | 0 1 2 8 1 8 4 | 1 4 8 8 4 8 1 | 4 4 8 2 4 2 | 4 1 2 1 --------------+------+------------+------------------------+--------------------------------------+-----------------------------------+---------------------------+-------------- x3o . . . . . | 3 | 3 0 | 2240 * * * | 1 6 0 0 0 0 0 | 6 12 0 0 0 0 0 | 12 8 0 0 0 0 | 8 1 0 0 x . . x . . . | 4 | 2 2 | * 20160 * * | 0 1 1 4 0 0 0 | 1 4 4 4 0 0 0 | 4 4 4 1 0 0 | 4 1 1 0 . . o3x . . . | 3 | 0 3 | * * 13440 * | 0 0 1 0 1 4 0 | 1 0 4 0 4 4 0 | 4 0 4 0 4 1 | 4 0 1 1 . . . x3o . . | 3 | 0 3 | * * * 26880 | 0 0 0 2 0 2 2 | 0 1 2 4 1 4 1 | 1 2 4 2 2 2 | 2 1 2 1 --------------+------+------------+------------------------+--------------------------------------+-----------------------------------+---------------------------+-------------- x3o3o . . . . ♦ 4 | 6 0 | 4 0 0 0 | 560 * * * * * * ♦ 6 0 0 0 0 0 0 | 12 0 0 0 0 0 | 8 0 0 0 x3o . x . . . ♦ 6 | 6 3 | 2 3 0 0 | * 6720 * * * * * | 1 4 0 0 0 0 0 | 4 4 0 0 0 0 | 4 1 0 0 x . o3x . . . ♦ 6 | 3 6 | 0 3 2 0 | * * 6720 * * * * | 1 0 4 0 0 0 0 | 4 0 4 0 0 0 | 4 0 1 0 x . . x3o . . ♦ 6 | 3 6 | 0 3 0 2 | * * * 26880 * * * | 0 1 1 2 0 0 0 | 1 2 2 1 0 0 | 2 1 1 0 . o3o3x . . . ♦ 4 | 0 6 | 0 0 4 0 | * * * * 3360 * * | 1 0 0 0 4 0 0 | 4 0 0 0 4 0 | 4 0 0 1 . . o3x3o . . ♦ 6 | 0 12 | 0 0 4 4 | * * * * * 13440 * | 0 0 1 0 1 2 0 | 1 0 2 0 2 1 | 2 0 1 1 . . . x3o3o . ♦ 4 | 0 6 | 0 0 0 4 | * * * * * * 13440 | 0 0 0 2 0 2 1 | 0 1 2 2 1 2 | 1 1 2 1 --------------+------+------------+------------------------+--------------------------------------+-----------------------------------+---------------------------+-------------- x3o3o3x . . . ♦ 20 | 30 30 | 20 30 20 0 | 5 10 10 0 5 0 0 | 672 * * * * * * | 4 0 0 0 0 0 | 4 0 0 0 x3o . x3o . . ♦ 9 | 9 9 | 3 9 0 3 | 0 3 0 3 0 0 0 | * 8960 * * * * * | 1 2 0 0 0 0 | 2 1 0 0 x . o3x3o . . ♦ 12 | 6 24 | 0 12 8 8 | 0 0 4 4 0 2 0 | * * 6720 * * * * | 1 0 2 0 0 0 | 2 0 1 0 x . . x3o3o . ♦ 8 | 4 12 | 0 6 0 8 | 0 0 0 4 0 0 2 | * * * 13440 * * * | 0 1 1 1 0 0 | 1 1 1 0 . o3o3x3o . . ♦ 10 | 0 30 | 0 0 20 10 | 0 0 0 0 5 5 0 | * * * * 2688 * * | 1 0 0 0 2 0 | 2 0 0 1 . . o3x3o3o . ♦ 10 | 0 30 | 0 0 10 20 | 0 0 0 0 0 5 5 | * * * * * 5376 * | 0 0 1 0 1 1 | 1 0 1 1 . . . x3o3o4o ♦ 8 | 0 24 | 0 0 0 32 | 0 0 0 0 0 0 16 | * * * * * * 840 | 0 0 0 2 0 2 | 0 1 2 1 --------------+------+------------+------------------------+--------------------------------------+-----------------------------------+---------------------------+-------------- x3o3o3x3o . . ♦ 60 | 90 180 | 60 180 120 60 | 15 60 60 60 30 30 0 | 6 20 15 0 6 0 0 | 448 * * * * * | 2 0 0 0 x3o . x3o3o . ♦ 12 | 12 18 | 4 18 0 12 | 0 6 0 12 0 0 3 | 0 4 0 3 0 0 0 | * 4480 * * * * | 1 1 0 0 x . o3x3o3o . ♦ 20 | 10 60 | 0 30 20 40 | 0 0 10 20 0 10 10 | 0 0 5 5 0 2 0 | * * 2688 * * * | 1 0 1 0 x . . x3o3o4o ♦ 16 | 8 48 | 0 24 0 64 | 0 0 0 32 0 0 32 | 0 0 0 16 0 0 2 | * * * 840 * * | 0 1 1 0 . o3o3x3o3o . ♦ 20 | 0 90 | 0 0 60 60 | 0 0 0 0 15 30 15 | 0 0 0 0 6 6 0 | * * * * 896 * | 1 0 0 1 . . o3x3o3o4o ♦ 40 | 0 240 | 0 0 80 320 | 0 0 0 0 0 80 160 | 0 0 0 0 0 32 10 | * * * * * 168 | 0 0 1 1 --------------+------+------------+------------------------+--------------------------------------+-----------------------------------+---------------------------+-------------- x3o3o3x3o3o . ♦ 140 | 210 630 | 140 630 420 420 | 35 210 210 420 105 210 105 | 21 140 105 105 42 42 0 | 7 35 21 0 7 0 | 128 * * * x3o . x3o3o4o ♦ 24 | 24 72 | 8 72 0 96 | 0 24 0 96 0 0 48 | 0 32 0 48 0 0 3 | 0 16 0 3 0 0 | * 280 * * x . o3x3o3o4o ♦ 80 | 40 480 | 0 240 160 640 | 0 0 80 320 0 160 320 | 0 0 80 160 0 64 20 | 0 0 32 10 0 2 | * * 84 * . o3o3x3o3o4o ♦ 160 | 0 1440 | 0 0 960 1920 | 0 0 0 0 240 960 960 | 0 0 0 0 192 384 60 | 0 0 0 0 64 12 | * * * 14
x3o3o3x3o3o4/3o . . . . . . . | 2240 | 3 18 | 3 36 18 36 | 1 18 18 72 6 36 24 | 6 36 36 48 12 24 3 | 12 24 24 6 8 3 | 8 3 3 1 ----------------+------+------------+------------------------+--------------------------------------+-----------------------------------+---------------------------+-------------- x . . . . . . | 2 | 3360 * | 2 12 0 0 | 1 12 6 24 0 0 0 | 6 24 12 16 0 0 0 | 12 16 8 2 0 0 | 8 2 1 0 . . . x . . . | 2 | * 20160 | 0 2 2 4 | 0 1 2 8 1 8 4 | 1 4 8 8 4 8 1 | 4 4 8 2 4 2 | 4 1 2 1 ----------------+------+------------+------------------------+--------------------------------------+-----------------------------------+---------------------------+-------------- x3o . . . . . | 3 | 3 0 | 2240 * * * | 1 6 0 0 0 0 0 | 6 12 0 0 0 0 0 | 12 8 0 0 0 0 | 8 1 0 0 x . . x . . . | 4 | 2 2 | * 20160 * * | 0 1 1 4 0 0 0 | 1 4 4 4 0 0 0 | 4 4 4 1 0 0 | 4 1 1 0 . . o3x . . . | 3 | 0 3 | * * 13440 * | 0 0 1 0 1 4 0 | 1 0 4 0 4 4 0 | 4 0 4 0 4 1 | 4 0 1 1 . . . x3o . . | 3 | 0 3 | * * * 26880 | 0 0 0 2 0 2 2 | 0 1 2 4 1 4 1 | 1 2 4 2 2 2 | 2 1 2 1 ----------------+------+------------+------------------------+--------------------------------------+-----------------------------------+---------------------------+-------------- x3o3o . . . . ♦ 4 | 6 0 | 4 0 0 0 | 560 * * * * * * ♦ 6 0 0 0 0 0 0 | 12 0 0 0 0 0 | 8 0 0 0 x3o . x . . . ♦ 6 | 6 3 | 2 3 0 0 | * 6720 * * * * * | 1 4 0 0 0 0 0 | 4 4 0 0 0 0 | 4 1 0 0 x . o3x . . . ♦ 6 | 3 6 | 0 3 2 0 | * * 6720 * * * * | 1 0 4 0 0 0 0 | 4 0 4 0 0 0 | 4 0 1 0 x . . x3o . . ♦ 6 | 3 6 | 0 3 0 2 | * * * 26880 * * * | 0 1 1 2 0 0 0 | 1 2 2 1 0 0 | 2 1 1 0 . o3o3x . . . ♦ 4 | 0 6 | 0 0 4 0 | * * * * 3360 * * | 1 0 0 0 4 0 0 | 4 0 0 0 4 0 | 4 0 0 1 . . o3x3o . . ♦ 6 | 0 12 | 0 0 4 4 | * * * * * 13440 * | 0 0 1 0 1 2 0 | 1 0 2 0 2 1 | 2 0 1 1 . . . x3o3o . ♦ 4 | 0 6 | 0 0 0 4 | * * * * * * 13440 | 0 0 0 2 0 2 1 | 0 1 2 2 1 2 | 1 1 2 1 ----------------+------+------------+------------------------+--------------------------------------+-----------------------------------+---------------------------+-------------- x3o3o3x . . . ♦ 20 | 30 30 | 20 30 20 0 | 5 10 10 0 5 0 0 | 672 * * * * * * | 4 0 0 0 0 0 | 4 0 0 0 x3o . x3o . . ♦ 9 | 9 9 | 3 9 0 3 | 0 3 0 3 0 0 0 | * 8960 * * * * * | 1 2 0 0 0 0 | 2 1 0 0 x . o3x3o . . ♦ 12 | 6 24 | 0 12 8 8 | 0 0 4 4 0 2 0 | * * 6720 * * * * | 1 0 2 0 0 0 | 2 0 1 0 x . . x3o3o . ♦ 8 | 4 12 | 0 6 0 8 | 0 0 0 4 0 0 2 | * * * 13440 * * * | 0 1 1 1 0 0 | 1 1 1 0 . o3o3x3o . . ♦ 10 | 0 30 | 0 0 20 10 | 0 0 0 0 5 5 0 | * * * * 2688 * * | 1 0 0 0 2 0 | 2 0 0 1 . . o3x3o3o . ♦ 10 | 0 30 | 0 0 10 20 | 0 0 0 0 0 5 5 | * * * * * 5376 * | 0 0 1 0 1 1 | 1 0 1 1 . . . x3o3o4/3o ♦ 8 | 0 24 | 0 0 0 32 | 0 0 0 0 0 0 16 | * * * * * * 840 | 0 0 0 2 0 2 | 0 1 2 1 ----------------+------+------------+------------------------+--------------------------------------+-----------------------------------+---------------------------+-------------- x3o3o3x3o . . ♦ 60 | 90 180 | 60 180 120 60 | 15 60 60 60 30 30 0 | 6 20 15 0 6 0 0 | 448 * * * * * | 2 0 0 0 x3o . x3o3o . ♦ 12 | 12 18 | 4 18 0 12 | 0 6 0 12 0 0 3 | 0 4 0 3 0 0 0 | * 4480 * * * * | 1 1 0 0 x . o3x3o3o . ♦ 20 | 10 60 | 0 30 20 40 | 0 0 10 20 0 10 10 | 0 0 5 5 0 2 0 | * * 2688 * * * | 1 0 1 0 x . . x3o3o4/3o ♦ 16 | 8 48 | 0 24 0 64 | 0 0 0 32 0 0 32 | 0 0 0 16 0 0 2 | * * * 840 * * | 0 1 1 0 . o3o3x3o3o . ♦ 20 | 0 90 | 0 0 60 60 | 0 0 0 0 15 30 15 | 0 0 0 0 6 6 0 | * * * * 896 * | 1 0 0 1 . . o3x3o3o4/3o ♦ 40 | 0 240 | 0 0 80 320 | 0 0 0 0 0 80 160 | 0 0 0 0 0 32 10 | * * * * * 168 | 0 0 1 1 ----------------+------+------------+------------------------+--------------------------------------+-----------------------------------+---------------------------+-------------- x3o3o3x3o3o . ♦ 140 | 210 630 | 140 630 420 420 | 35 210 210 420 105 210 105 | 21 140 105 105 42 42 0 | 7 35 21 0 7 0 | 128 * * * x3o . x3o3o4/3o ♦ 24 | 24 72 | 8 72 0 96 | 0 24 0 96 0 0 48 | 0 32 0 48 0 0 3 | 0 16 0 3 0 0 | * 280 * * x . o3x3o3o4/3o ♦ 80 | 40 480 | 0 240 160 640 | 0 0 80 320 0 160 320 | 0 0 80 160 0 64 20 | 0 0 32 10 0 2 | * * 84 * . o3o3x3o3o4/3o ♦ 160 | 0 1440 | 0 0 960 1920 | 0 0 0 0 240 960 960 | 0 0 0 0 192 384 60 | 0 0 0 0 64 12 | * * * 14
o3o3o *b3x3o3o3x . . . . . . . | 2240 | 18 3 | 36 18 36 3 | 12 12 36 72 6 18 18 1 | 3 12 24 12 24 12 36 36 6 | 3 6 4 12 12 4 12 12 12 | 1 3 3 4 4 -----------------+------+------------+------------------------+------------------------------------------+--------------------------------------------+-----------------------------------------+---------------- . . . x . . . | 2 | 20160 * | 4 2 2 0 | 2 2 8 8 1 2 1 0 | 1 4 4 4 4 4 8 4 1 | 2 2 2 4 2 2 4 2 4 | 1 2 1 2 2 . . . . . . x | 2 | * 3360 | 0 0 12 2 | 0 0 0 24 0 6 12 1 | 0 0 8 0 8 0 12 24 6 | 0 2 0 4 8 0 4 8 12 | 0 1 2 4 4 -----------------+------+------------+------------------------+------------------------------------------+--------------------------------------------+-----------------------------------------+---------------- . o . *b3x . . . | 3 | 3 0 | 26880 * * * | 1 1 2 2 0 0 0 0 | 1 2 2 2 2 1 2 1 0 | 2 2 1 2 1 1 2 1 1 | 1 2 1 1 1 . . . x3o . . | 3 | 3 0 | * 13440 * * | 0 0 4 0 1 1 0 0 | 0 2 0 2 0 4 4 0 1 | 1 0 2 2 0 2 2 0 4 | 1 1 0 2 2 . . . x . . x | 4 | 2 2 | * * 20160 * | 0 0 0 4 0 1 1 0 | 0 0 2 0 2 0 4 4 1 | 0 1 0 2 2 0 2 2 4 | 0 1 1 2 2 . . . . . o3x | 3 | 0 3 | * * * 2240 | 0 0 0 0 0 0 6 1 | 0 0 0 0 0 0 0 12 6 | 0 0 0 0 4 0 0 4 12 | 0 0 1 4 4 -----------------+------+------------+------------------------+------------------------------------------+--------------------------------------------+-----------------------------------------+---------------- o3o . *b3x . . . ♦ 4 | 6 0 | 4 0 0 0 | 6720 * * * * * * * | 1 2 2 0 0 0 0 0 0 | 2 2 1 2 1 0 0 0 0 | 1 2 1 1 0 . o3o *b3x . . . ♦ 4 | 6 0 | 4 0 0 0 | * 6720 * * * * * * | 1 0 0 2 2 0 0 0 0 | 2 2 0 0 0 1 2 1 0 | 1 2 1 0 1 . o . *b3x3o . . ♦ 6 | 12 0 | 4 4 0 0 | * * 13440 * * * * * | 0 1 0 1 0 1 1 0 0 | 1 0 1 1 0 1 1 0 1 | 1 1 0 1 1 . o . *b3x . . x ♦ 6 | 6 3 | 2 0 3 0 | * * * 26880 * * * * | 0 0 1 0 1 0 1 1 0 | 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 . . . x3o3o . ♦ 4 | 6 0 | 0 4 0 0 | * * * * 3360 * * * | 0 0 0 0 0 4 0 0 1 | 0 0 2 0 0 2 0 0 4 | 1 0 0 2 2 . . . x3o . x ♦ 6 | 6 3 | 0 2 3 0 | * * * * * 6720 * * | 0 0 0 0 0 0 4 0 1 | 0 0 0 2 0 0 2 0 4 | 0 1 0 2 2 . . . x . o3x ♦ 6 | 3 6 | 0 0 3 2 | * * * * * * 6720 * | 0 0 0 0 0 0 0 4 1 | 0 0 0 0 2 0 0 2 4 | 0 0 1 2 2 . . . . o3o3x ♦ 4 | 0 6 | 0 0 0 4 | * * * * * * * 560 ♦ 0 0 0 0 0 0 0 0 6 | 0 0 0 0 0 0 0 0 12 | 0 0 0 4 4 -----------------+------+------------+------------------------+------------------------------------------+--------------------------------------------+-----------------------------------------+---------------- o3o3o *b3x . . . ♦ 8 | 24 0 | 32 0 0 0 | 8 8 0 0 0 0 0 0 | 840 * * * * * * * * | 2 2 0 0 0 0 0 0 0 | 1 2 1 0 0 o3o . *b3x3o . . ♦ 10 | 30 0 | 20 10 0 0 | 5 0 5 0 0 0 0 0 | * 2688 * * * * * * * | 1 0 1 1 0 0 0 0 0 | 1 1 0 1 0 o3o . *b3x . . x ♦ 8 | 12 4 | 8 0 6 0 | 2 0 0 4 0 0 0 0 | * * 6720 * * * * * * | 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 . o3o *b3x3o . . ♦ 10 | 30 0 | 20 10 0 0 | 0 5 5 0 0 0 0 0 | * * * 2688 * * * * * | 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . o3o *b3x . . x ♦ 8 | 12 4 | 8 0 6 0 | 0 2 0 4 0 0 0 0 | * * * * 6720 * * * * | 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 . o . *b3x3o3o . ♦ 10 | 30 0 | 10 20 0 0 | 0 0 5 0 5 0 0 0 | * * * * * 2688 * * * | 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 . o . *b3x3o . x ♦ 12 | 24 6 | 8 8 12 0 | 0 0 2 4 0 4 0 0 | * * * * * * 6720 * * | 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 . o . *b3x . o3x ♦ 9 | 9 9 | 3 0 9 3 | 0 0 0 3 0 0 3 0 | * * * * * * * 8960 * | 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 . . . x3o3o3x ♦ 20 | 30 30 | 0 20 30 20 | 0 0 0 0 5 10 10 5 | * * * * * * * * 672 | 0 0 0 0 0 0 0 0 4 | 0 0 0 2 2 -----------------+------+------------+------------------------+------------------------------------------+--------------------------------------------+-----------------------------------------+---------------- o3o3o *b3x3o . . ♦ 40 | 240 0 | 320 80 0 0 | 80 80 80 0 0 0 0 0 | 10 16 0 16 0 0 0 0 0 | 168 * * * * * * * * | 1 1 0 0 0 o3o3o *b3x . . x ♦ 16 | 48 8 | 64 0 24 0 | 16 16 0 32 0 0 0 0 | 2 0 8 0 8 0 0 0 0 | * 840 * * * * * * * | 0 1 1 0 0 o3o . *b3x3o3o . ♦ 20 | 90 0 | 60 60 0 0 | 15 0 30 0 15 0 0 0 | 0 6 0 0 0 6 0 0 0 | * * 448 * * * * * * | 1 0 0 1 0 o3o . *b3x3o . x ♦ 20 | 60 10 | 40 20 30 0 | 10 0 10 20 0 10 0 0 | 0 2 5 0 0 0 5 0 0 | * * * 1344 * * * * * | 0 1 0 1 0 o3o . *b3x . o3x ♦ 12 | 18 12 | 12 0 18 4 | 3 0 0 12 0 0 6 0 | 0 0 3 0 0 0 0 4 0 | * * * * 2240 * * * * | 0 0 1 1 0 . o3o *b3x3o3o . ♦ 20 | 90 0 | 60 60 0 0 | 0 15 30 0 15 0 0 0 | 0 0 0 6 0 6 0 0 0 | * * * * * 448 * * * | 1 0 0 0 1 . o3o *b3x3o . x ♦ 20 | 60 10 | 40 20 30 0 | 0 10 10 20 0 10 0 0 | 0 0 0 2 5 0 5 0 0 | * * * * * * 1344 * * | 0 1 0 0 1 . o3o *b3x . o3x ♦ 12 | 18 12 | 12 0 18 4 | 0 3 0 12 0 0 6 0 | 0 0 0 0 3 0 0 4 0 | * * * * * * * 2240 * | 0 0 1 0 1 . o . *b3x3o3o3x ♦ 60 | 180 90 | 60 120 180 60 | 0 0 30 60 30 60 60 15 | 0 0 0 0 0 6 15 20 6 | * * * * * * * * 448 | 0 0 0 1 1 -----------------+------+------------+------------------------+------------------------------------------+--------------------------------------------+-----------------------------------------+---------------- o3o3o *b3x3o3o . ♦ 160 | 1440 0 | 1920 960 0 0 | 480 480 960 0 240 0 0 0 | 60 192 0 192 0 192 0 0 0 | 12 0 32 0 0 32 0 0 0 | 14 * * * * o3o3o *b3x3o . x ♦ 80 | 480 40 | 640 160 240 0 | 160 160 160 320 0 80 0 0 | 20 32 80 32 80 0 80 0 0 | 2 10 0 16 0 0 16 0 0 | * 84 * * * o3o3o *b3x . o3x ♦ 24 | 72 24 | 96 0 72 8 | 24 24 0 96 0 0 24 0 | 3 0 24 0 24 0 0 32 0 | 0 3 0 0 8 0 0 8 0 | * * 280 * * o3o . *b3x3o3o3x ♦ 140 | 630 210 | 420 420 630 140 | 105 0 210 420 105 210 210 35 | 0 42 105 0 0 42 105 140 21 | 0 0 7 21 35 0 0 0 7 | * * * 64 * . o3o *b3x3o3o3x ♦ 140 | 630 210 | 420 420 630 140 | 0 105 210 420 105 210 210 35 | 0 0 0 42 105 42 105 140 21 | 0 0 0 0 0 7 21 35 7 | * * * * 64
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