runcinated hexacross
- general polytopal classes:
- Wythoffian polypeta lace simplices
links
| Acronym | spog |
| Name |
small prismatohexacontitetrapeton, runcinated hexacross |
| Circumradius | sqrt(7/2) = 1.870829 |
| Coordinates | (sqrt(2), 1/sqrt(2), 1/sqrt(2), 1/sqrt(2), 0, 0) & all permutations, all changes of sign |
| Face vector | 960, 7200, 14400, 11280, 3416, 296 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3o3o3x3o4o . . . . . . | 960 | 3 12 | 3 24 12 12 | 1 12 12 24 4 12 3 | 4 12 12 6 4 3 | 4 3 3 1 ------------+-----+-----------+--------------------+---------------------------------+--------------------------+------------- x . . . . . | 2 | 1440 * | 2 8 0 0 | 1 8 4 2 0 0 0 | 4 8 4 2 0 0 | 4 2 1 0 . . . x . . | 2 | * 5760 | 0 2 2 2 | 0 1 2 4 1 4 1 | 1 2 4 2 2 2 | 2 1 2 1 ------------+-----+-----------+--------------------+---------------------------------+--------------------------+------------- x3o . . . . | 3 | 3 0 | 960 * * * | 1 4 0 0 0 0 0 | 4 4 0 0 0 0 | 4 1 0 0 x . . x . . | 4 | 2 2 | * 5760 * * | 0 1 1 2 0 0 0 | 1 2 2 1 0 0 | 2 1 1 0 . . o3x . . | 3 | 0 3 | * * 3840 * | 0 0 1 0 1 2 0 | 1 0 2 0 2 1 | 2 0 1 1 . . . x3o . | 3 | 0 3 | * * * 3840 | 0 0 0 2 0 2 1 | 0 1 2 2 1 2 | 1 1 2 1 ------------+-----+-----------+--------------------+---------------------------------+--------------------------+------------- x3o3o . . . ♦ 4 | 6 0 | 4 0 0 0 | 240 * * * * * * | 4 0 0 0 0 0 | 4 0 0 0 x3o . x . . ♦ 6 | 6 3 | 2 3 0 0 | * 1920 * * * * * | 1 2 0 0 0 0 | 2 1 0 0 x . o3x . . ♦ 6 | 3 6 | 0 3 2 0 | * * 1920 * * * * | 1 0 2 0 0 0 | 2 0 1 0 x . . x3o . ♦ 6 | 3 6 | 0 3 0 2 | * * * 3840 * * * | 0 1 1 1 0 0 | 1 1 1 0 . o3o3x . . ♦ 4 | 0 6 | 0 0 4 0 | * * * * 960 * * | 1 0 0 0 2 0 | 2 0 0 1 . . o3x3o . ♦ 6 | 0 12 | 0 0 4 4 | * * * * * 1920 * | 0 0 1 0 1 1 | 1 0 1 1 . . . x3o4o ♦ 6 | 0 12 | 0 0 0 8 | * * * * * * 480 | 0 0 0 2 0 2 | 0 1 2 1 ------------+-----+-----------+--------------------+---------------------------------+--------------------------+------------- x3o3o3x . . ♦ 20 | 30 30 | 20 30 20 0 | 5 10 10 0 5 0 0 | 192 * * * * * | 2 0 0 0 x3o . x3o . ♦ 9 | 9 9 | 3 9 0 3 | 0 3 0 3 0 0 0 | * 1280 * * * * | 1 1 0 0 x . o3x3o . ♦ 12 | 6 24 | 0 12 8 8 | 0 0 4 4 0 2 0 | * * 960 * * * | 1 0 1 0 x . . x3o4o ♦ 12 | 6 24 | 0 12 0 16 | 0 0 0 8 0 0 2 | * * * 480 * * | 0 1 1 0 . o3o3x3o . ♦ 10 | 0 30 | 0 0 20 10 | 0 0 0 0 5 5 0 | * * * * 384 * | 1 0 0 1 . . o3x3o4o ♦ 24 | 0 96 | 0 0 32 64 | 0 0 0 0 0 16 8 | * * * * * 120 | 0 0 1 1 ------------+-----+-----------+--------------------+---------------------------------+--------------------------+------------- x3o3o3x3o . ♦ 60 | 90 180 | 60 180 120 60 | 15 60 60 60 30 30 0 | 6 20 15 0 6 0 | 64 * * * x3o . x3o4o ♦ 18 | 18 36 | 6 36 0 24 | 0 12 0 24 0 0 3 | 0 8 0 3 0 0 | * 160 * * x . o3x3o4o ♦ 48 | 24 192 | 0 96 64 128 | 0 0 32 64 0 32 16 | 0 0 16 8 0 2 | * * 60 * . o3o3x3o4o ♦ 80 | 0 480 | 0 0 320 320 | 0 0 0 0 80 160 40 | 0 0 0 0 32 10 | * * * 12
x3o3o3x3o4/3o . . . . . . | 960 | 3 12 | 3 24 12 12 | 1 12 12 24 4 12 3 | 4 12 12 6 4 3 | 4 3 3 1 --------------+-----+-----------+--------------------+---------------------------------+--------------------------+------------- x . . . . . | 2 | 1440 * | 2 8 0 0 | 1 8 4 2 0 0 0 | 4 8 4 2 0 0 | 4 2 1 0 . . . x . . | 2 | * 5760 | 0 2 2 2 | 0 1 2 4 1 4 1 | 1 2 4 2 2 2 | 2 1 2 1 --------------+-----+-----------+--------------------+---------------------------------+--------------------------+------------- x3o . . . . | 3 | 3 0 | 960 * * * | 1 4 0 0 0 0 0 | 4 4 0 0 0 0 | 4 1 0 0 x . . x . . | 4 | 2 2 | * 5760 * * | 0 1 1 2 0 0 0 | 1 2 2 1 0 0 | 2 1 1 0 . . o3x . . | 3 | 0 3 | * * 3840 * | 0 0 1 0 1 2 0 | 1 0 2 0 2 1 | 2 0 1 1 . . . x3o . | 3 | 0 3 | * * * 3840 | 0 0 0 2 0 2 1 | 0 1 2 2 1 2 | 1 1 2 1 --------------+-----+-----------+--------------------+---------------------------------+--------------------------+------------- x3o3o . . . ♦ 4 | 6 0 | 4 0 0 0 | 240 * * * * * * | 4 0 0 0 0 0 | 4 0 0 0 x3o . x . . ♦ 6 | 6 3 | 2 3 0 0 | * 1920 * * * * * | 1 2 0 0 0 0 | 2 1 0 0 x . o3x . . ♦ 6 | 3 6 | 0 3 2 0 | * * 1920 * * * * | 1 0 2 0 0 0 | 2 0 1 0 x . . x3o . ♦ 6 | 3 6 | 0 3 0 2 | * * * 3840 * * * | 0 1 1 1 0 0 | 1 1 1 0 . o3o3x . . ♦ 4 | 0 6 | 0 0 4 0 | * * * * 960 * * | 1 0 0 0 2 0 | 2 0 0 1 . . o3x3o . ♦ 6 | 0 12 | 0 0 4 4 | * * * * * 1920 * | 0 0 1 0 1 1 | 1 0 1 1 . . . x3o4/3o ♦ 6 | 0 12 | 0 0 0 8 | * * * * * * 480 | 0 0 0 2 0 2 | 0 1 2 1 --------------+-----+-----------+--------------------+---------------------------------+--------------------------+------------- x3o3o3x . . ♦ 20 | 30 30 | 20 30 20 0 | 5 10 10 0 5 0 0 | 192 * * * * * | 2 0 0 0 x3o . x3o . ♦ 9 | 9 9 | 3 9 0 3 | 0 3 0 3 0 0 0 | * 1280 * * * * | 1 1 0 0 x . o3x3o . ♦ 12 | 6 24 | 0 12 8 8 | 0 0 4 4 0 2 0 | * * 960 * * * | 1 0 1 0 x . . x3o4/3o ♦ 12 | 6 24 | 0 12 0 16 | 0 0 0 8 0 0 2 | * * * 480 * * | 0 1 1 0 . o3o3x3o . ♦ 10 | 0 30 | 0 0 20 10 | 0 0 0 0 5 5 0 | * * * * 384 * | 1 0 0 1 . . o3x3o4/3o ♦ 24 | 0 96 | 0 0 32 64 | 0 0 0 0 0 16 8 | * * * * * 120 | 0 0 1 1 --------------+-----+-----------+--------------------+---------------------------------+--------------------------+------------- x3o3o3x3o . ♦ 60 | 90 180 | 60 180 120 60 | 15 60 60 60 30 30 0 | 6 20 15 0 6 0 | 64 * * * x3o . x3o4/3o ♦ 18 | 18 36 | 6 36 0 24 | 0 12 0 24 0 0 3 | 0 8 0 3 0 0 | * 160 * * x . o3x3o4/3o ♦ 48 | 24 192 | 0 96 64 128 | 0 0 32 64 0 32 16 | 0 0 16 8 0 2 | * * 60 * . o3o3x3o4/3o ♦ 80 | 0 480 | 0 0 320 320 | 0 0 0 0 80 160 40 | 0 0 0 0 32 10 | * * * 12
. . . . . . | 960 | 12 3 | 6 6 12 24 3 | 3 6 12 6 12 4 12 12 1 | 3 6 2 6 6 2 6 6 4 | 1 3 3 2 2 ---------------+-----+-----------+-------------------------+-----------------------------------------+-------------------------------------+---------------- . x . . . . | 2 | 5760 * | 1 1 2 2 0 | 1 2 2 2 2 1 2 1 0 | 2 2 1 2 1 1 2 1 1 | 1 2 1 1 1 . . . . . x | 2 | * 1440 | 0 0 0 8 2 | 0 0 4 0 4 0 4 8 1 | 0 2 0 2 4 0 2 4 4 | 0 1 2 2 2 ---------------+-----+-----------+-------------------------+-----------------------------------------+-------------------------------------+---------------- o3x . . . . | 3 | 3 0 | 1920 * * * * | 1 2 2 0 0 0 0 0 0 | 2 2 1 2 1 0 0 0 0 | 1 2 1 1 0 . x3o . . . | 3 | 3 0 | * 1920 * * * | 1 0 0 2 2 0 0 0 0 | 2 2 0 0 0 1 2 1 0 | 1 2 1 0 1 . x . *b3o . . | 3 | 3 0 | * * 3840 * * | 0 1 0 1 0 1 1 0 0 | 1 0 1 1 0 1 1 0 1 | 1 1 0 1 1 . x . . . x | 4 | 2 2 | * * * 5760 * | 0 0 1 0 1 0 1 1 0 | 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 . . . . o3x | 3 | 0 3 | * * * * 960 | 0 0 0 0 0 0 0 4 1 | 0 0 0 0 2 0 0 2 4 | 0 0 1 2 2 ---------------+-----+-----------+-------------------------+-----------------------------------------+-------------------------------------+---------------- o3x3o . . . ♦ 6 | 12 0 | 4 4 0 0 0 | 480 * * * * * * * * | 2 2 0 0 0 0 0 0 0 | 1 2 1 0 0 o3x . *b3o . . ♦ 6 | 12 0 | 4 0 4 0 0 | * 960 * * * * * * * | 1 0 1 1 0 0 0 0 0 | 1 1 0 1 0 o3x . . . x ♦ 6 | 6 3 | 2 0 0 3 0 | * * 1920 * * * * * * | 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 . x3o *b3o . . ♦ 6 | 12 0 | 0 4 4 0 0 | * * * 960 * * * * * | 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x3o . . x ♦ 6 | 6 3 | 0 2 0 3 0 | * * * * 1920 * * * * | 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 . x . *b3o3o . ♦ 4 | 6 0 | 0 0 4 0 0 | * * * * * 960 * * * | 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 . x . *b3o . x ♦ 6 | 6 3 | 0 0 2 3 0 | * * * * * * 1920 * * | 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 . x . . o3x ♦ 6 | 3 6 | 0 0 0 3 2 | * * * * * * * 1920 * | 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 . . . o3o3x ♦ 4 | 0 6 | 0 0 0 0 4 | * * * * * * * * 240 | 0 0 0 0 0 0 0 0 4 | 0 0 0 2 2 ---------------+-----+-----------+-------------------------+-----------------------------------------+-------------------------------------+---------------- o3x3o *b3o . . ♦ 24 | 96 0 | 32 32 32 0 0 | 8 8 0 8 0 0 0 0 0 | 120 * * * * * * * * | 1 1 0 0 0 o3x3o . . x ♦ 12 | 24 6 | 8 8 0 12 0 | 2 0 4 0 4 0 0 0 0 | * 480 * * * * * * * | 0 1 1 0 0 o3x . *b3o3o . ♦ 10 | 30 0 | 10 0 20 0 0 | 0 5 0 0 0 5 0 0 0 | * * 192 * * * * * * | 1 0 0 1 0 o3x . *b3o . x ♦ 12 | 24 6 | 8 0 8 12 0 | 0 2 4 0 0 0 4 0 0 | * * * 480 * * * * * | 0 1 0 1 0 o3x . . o3x ♦ 9 | 9 9 | 3 0 0 9 3 | 0 0 3 0 0 0 0 3 0 | * * * * 640 * * * * | 0 0 1 1 0 . x3o *b3o3o . ♦ 10 | 30 0 | 0 10 20 0 0 | 0 0 0 5 0 5 0 0 0 | * * * * * 192 * * * | 1 0 0 0 1 . x3o *b3o . x ♦ 12 | 24 6 | 0 8 8 12 0 | 0 0 0 2 4 0 4 0 0 | * * * * * * 480 * * | 0 1 0 0 1 . x3o . o3x ♦ 9 | 9 9 | 0 3 0 9 3 | 0 0 0 0 3 0 0 3 0 | * * * * * * * 640 * | 0 0 1 0 1 . x . *b3o3o3x ♦ 20 | 30 30 | 0 0 20 30 20 | 0 0 0 0 0 5 10 10 5 | * * * * * * * * 192 | 0 0 0 1 1 ---------------+-----+-----------+-------------------------+-----------------------------------------+-------------------------------------+---------------- o3x3o *b3o3o . ♦ 80 | 480 0 | 160 160 320 0 0 | 40 80 0 80 0 80 0 0 0 | 10 0 16 0 0 16 0 0 0 | 12 * * * * o3x3o *b3o . x ♦ 48 | 192 24 | 64 64 64 96 0 | 16 16 32 16 32 0 32 0 0 | 2 8 0 8 0 0 8 0 0 | * 60 * * * o3x3o . o3x ♦ 18 | 36 18 | 12 12 0 36 6 | 3 0 12 0 12 0 0 12 0 | 0 3 0 0 4 0 0 4 0 | * * 160 * * o3x . *b3o3o3x ♦ 60 | 180 90 | 60 0 120 180 60 | 0 30 60 0 0 30 60 60 15 | 0 0 6 15 20 0 0 0 6 | * * * 32 * . x3o *b3o3o3x ♦ 60 | 180 90 | 0 60 120 180 60 | 0 0 0 30 60 30 60 60 15 | 0 0 0 0 0 6 15 20 6 | * * * * 32
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