(small hebdomecontadiaprismated pentacontitetrapeton)
wrt. tratrip
wrt. scad
wrt. spiddip
wrt. siphin
- general polytopal classes:
- Wythoffian polypeta lace simplices
- analogs:
- all-ends expanded Gossetic eEn
links
| Acronym | spam (old: skopam) |
| Name |
small prismated pentacontitetrapeton, (small hebdomecontadiaprismated pentacontitetrapeton) |
| Circumradius | sqrt(5) = 2.236068 |
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Inradius wrt. tratrip | 7/sqrt(12) = 2.020726 |
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Inradius wrt. scad | 2 |
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Inradius wrt. spiddip | sqrt(15)/2 = 1.936492 |
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Inradius wrt. siphin | sqrt(27/8) = 1.837117 |
| Volume | 17811 sqrt(3)/80 = 385.619462 |
| Surface | [2700+4203 sqrt(2)+756 sqrt(3)+6300 sqrt(5)]/20 = 1202.029914 |
| Dihedral angles | |
| Face vector | 2160, 15120, 36720, 36720, 14238, 1278 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3o3o3o3x *c3x . . . . . . | 2160 | 4 4 6 | 6 12 12 12 6 12 | 4 12 6 12 12 24 4 4 4 12 6 | 1 4 4 6 12 4 4 12 12 1 1 4 4 | 1 1 4 6 4 1 ---------------+------+----------------+-------------------------------+--------------------------------------------------------+-------------------------------------------------------------+--------------------- x . . . . . | 2 | 4320 * * | 3 3 3 0 0 0 | 3 6 3 3 3 6 0 0 0 0 0 | 1 3 3 3 6 1 1 3 3 0 0 0 0 | 1 1 3 3 1 1 . . . . x . | 2 | * 4320 * | 0 3 0 0 3 3 | 0 3 0 0 6 6 0 3 0 3 3 | 0 1 0 3 3 3 0 3 6 1 0 1 3 | 1 0 1 3 3 1 . . . . . x | 2 | * * 6480 | 0 0 2 4 0 2 | 0 0 1 4 0 4 2 0 2 4 1 | 0 0 2 0 2 0 2 4 2 0 1 2 2 | 0 1 2 1 2 1 ---------------+------+----------------+-------------------------------+--------------------------------------------------------+-------------------------------------------------------------+--------------------- x3o . . . . | 3 | 3 0 0 | 4320 * * * * * | 2 2 1 0 0 0 0 0 0 0 0 | 1 2 2 1 2 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 x . . . x . | 4 | 2 2 0 | * 6480 * * * * | 0 2 0 0 2 2 0 0 0 0 0 | 0 1 0 2 2 1 0 1 2 0 0 0 0 | 1 0 1 2 1 0 x . . . . x | 4 | 2 0 2 | * * 6480 * * * | 0 0 1 2 0 2 0 0 0 0 0 | 0 0 2 0 2 0 1 2 1 0 0 0 0 | 0 1 2 1 1 0 . . o . . *c3x | 3 | 0 0 3 | * * * 8640 * * | 0 0 0 1 0 0 1 0 1 1 0 | 0 0 1 0 0 0 1 1 0 0 1 1 1 | 0 1 1 0 1 1 . . . o3x . | 3 | 0 3 0 | * * * * 4320 * | 0 0 0 0 2 0 0 2 0 0 1 | 0 0 0 1 0 2 0 0 2 1 0 0 2 | 1 0 0 1 2 1 . . . . x x | 4 | 0 2 2 | * * * * * 6480 | 0 0 0 0 0 2 0 0 0 2 1 | 0 0 0 0 1 0 0 2 2 0 0 1 2 | 0 0 1 1 2 1 ---------------+------+----------------+-------------------------------+--------------------------------------------------------+-------------------------------------------------------------+--------------------- x3o3o . . . ♦ 4 | 6 0 0 | 4 0 0 0 0 0 | 2160 * * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 x3o . . x . ♦ 6 | 6 3 0 | 2 3 0 0 0 0 | * 4320 * * * * * * * * * | 0 1 0 1 1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0 x3o . . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 | * * 2160 * * * * * * * * | 0 0 2 0 2 0 0 0 0 0 0 0 0 | 0 1 2 1 0 0 x . o . . *c3x ♦ 6 | 3 0 6 | 0 0 3 2 0 0 | * * * 4320 * * * * * * * | 0 0 1 0 0 0 1 1 0 0 0 0 0 | 0 1 1 0 1 0 x . . o3x . ♦ 6 | 3 6 0 | 0 3 0 0 2 0 | * * * * 4320 * * * * * * | 0 0 0 1 0 1 0 0 1 0 0 0 0 | 1 0 0 1 1 0 x . . . x x ♦ 8 | 4 4 4 | 0 2 2 0 0 2 | * * * * * 6480 * * * * * | 0 0 0 0 1 0 0 1 1 0 0 0 0 | 0 0 1 1 1 0 . o3o . . *c3x ♦ 4 | 0 0 6 | 0 0 0 4 0 0 | * * * * * * 2160 * * * * | 0 0 1 0 0 0 0 0 0 0 1 1 0 | 0 1 1 0 0 1 . . o3o3x . ♦ 4 | 0 6 0 | 0 0 0 0 4 0 | * * * * * * * 2160 * * * | 0 0 0 0 0 1 0 0 0 1 0 0 1 | 1 0 0 0 1 1 . . o3o . *c3x ♦ 4 | 0 0 6 | 0 0 0 4 0 0 | * * * * * * * * 2160 * * | 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 1 0 0 1 1 . . o . x *c3x ♦ 6 | 0 3 6 | 0 0 0 2 0 3 | * * * * * * * * * 4320 * | 0 0 0 0 0 0 0 1 0 0 0 1 1 | 0 0 1 0 1 1 . . . o3x x ♦ 6 | 0 6 3 | 0 0 0 0 2 3 | * * * * * * * * * * 2160 | 0 0 0 0 0 0 0 0 2 0 0 0 2 | 0 0 0 1 2 1 ---------------+------+----------------+-------------------------------+--------------------------------------------------------+-------------------------------------------------------------+--------------------- x3o3o3o . . ♦ 5 | 10 0 0 | 10 0 0 0 0 0 | 5 0 0 0 0 0 0 0 0 0 0 | 432 * * * * * * * * * * * * | 1 1 0 0 0 0 x3o3o . x . ♦ 8 | 12 4 0 | 8 6 0 0 0 0 | 2 4 0 0 0 0 0 0 0 0 0 | * 1080 * * * * * * * * * * * | 1 0 1 0 0 0 x3o3o . . *c3x ♦ 20 | 30 0 30 | 20 0 30 20 0 0 | 5 0 10 10 0 0 5 0 0 0 0 | * * 432 * * * * * * * * * * | 0 1 1 0 0 0 x3o . o3x . ♦ 9 | 9 9 0 | 3 9 0 0 3 0 | 0 3 0 0 3 0 0 0 0 0 0 | * * * 1440 * * * * * * * * * | 1 0 0 1 0 0 x3o . . x x ♦ 12 | 12 6 6 | 4 6 6 0 0 3 | 0 2 2 0 0 3 0 0 0 0 0 | * * * * 2160 * * * * * * * * | 0 0 1 1 0 0 x . o3o3x . ♦ 8 | 4 12 0 | 0 6 0 0 8 0 | 0 0 0 0 4 0 0 2 0 0 0 | * * * * * 1080 * * * * * * * | 1 0 0 0 1 0 x . o3o . *c3x ♦ 8 | 4 0 12 | 0 0 6 8 0 0 | 0 0 0 4 0 0 0 0 2 0 0 | * * * * * * 1080 * * * * * * | 0 1 0 0 1 0 x . o . x *c3x ♦ 12 | 6 6 12 | 0 3 6 4 0 6 | 0 0 0 2 0 3 0 0 0 2 0 | * * * * * * * 2160 * * * * * | 0 0 1 0 1 0 x . . o3x x ♦ 12 | 6 12 6 | 0 6 3 0 4 6 | 0 0 0 0 2 3 0 0 0 0 2 | * * * * * * * * 2160 * * * * | 0 0 0 1 1 0 . o3o3o3x . ♦ 5 | 0 10 0 | 0 0 0 0 10 0 | 0 0 0 0 0 0 0 5 0 0 0 | * * * * * * * * * 432 * * * | 1 0 0 0 0 1 . o3o3o . *c3x ♦ 8 | 0 0 24 | 0 0 0 32 0 0 | 0 0 0 0 0 0 8 0 8 0 0 | * * * * * * * * * * 270 * * | 0 1 0 0 0 1 . o3o . x *c3x ♦ 8 | 0 4 12 | 0 0 0 8 0 6 | 0 0 0 0 0 0 2 0 0 4 0 | * * * * * * * * * * * 1080 * | 0 0 1 0 0 1 . . o3o3x *c3x ♦ 20 | 0 30 30 | 0 0 0 20 20 30 | 0 0 0 0 0 0 0 5 5 10 10 | * * * * * * * * * * * * 432 | 0 0 0 0 1 1 ---------------+------+----------------+-------------------------------+--------------------------------------------------------+-------------------------------------------------------------+--------------------- x3o3o3o3x . ♦ 30 | 60 60 0 | 60 90 0 0 60 0 | 30 60 0 0 60 0 0 30 0 0 0 | 6 15 0 20 0 15 0 0 0 6 0 0 0 | 72 * * * * * x3o3o3o . *c3x ♦ 80 | 160 0 240 | 160 0 240 320 0 0 | 80 0 80 160 0 0 80 0 80 0 0 | 16 0 16 0 0 0 40 0 0 0 10 0 0 | * 27 * * * * x3o3o . x *c3x ♦ 40 | 60 20 60 | 40 30 60 40 0 30 | 10 20 20 20 0 30 10 0 0 20 0 | 0 5 2 0 10 0 0 10 0 0 0 5 0 | * * 216 * * * x3o . o3x x ♦ 18 | 18 18 9 | 6 18 9 0 6 9 | 0 6 3 0 6 9 0 0 0 0 3 | 0 0 0 2 3 0 0 0 3 0 0 0 0 | * * * 720 * * x . o3o3x *c3x ♦ 40 | 20 60 60 | 0 30 30 40 40 60 | 0 0 0 20 20 30 0 10 10 20 20 | 0 0 0 0 0 5 5 10 10 0 0 0 2 | * * * * 216 * . o3o3o3x *c3x ♦ 80 | 0 160 240 | 0 0 0 320 160 240 | 0 0 0 0 0 0 80 80 80 160 80 | 0 0 0 0 0 0 0 0 0 16 10 40 16 | * * * * * 27
or . . . . . . | 2160 | 8 6 | 12 12 24 12 | 8 24 12 24 24 8 | 2 8 8 6 24 8 12 1 | 1 2 8 6 ------------------+------+-----------+----------------------+-------------------------------+--------------------------------------+-------------- x . . . . . & | 2 | 8640 * | 3 3 3 0 | 3 9 3 3 6 0 | 1 4 3 3 9 1 3 0 | 1 1 4 3 . . . . . x | 2 | * 6480 | 0 0 4 4 | 0 0 2 8 4 4 | 0 0 4 0 4 4 4 1 | 0 2 4 1 ------------------+------+-----------+----------------------+-------------------------------+--------------------------------------+-------------- x3o . . . . & | 3 | 3 0 | 8640 * * * | 2 2 1 0 0 0 | 1 2 2 1 2 0 0 0 | 1 1 2 1 x . . . x . | 4 | 4 0 | * 6480 * * | 0 4 0 0 2 0 | 0 2 0 2 4 0 1 0 | 1 0 2 2 x . . . . x & | 4 | 2 2 | * * 12960 * | 0 0 1 2 2 0 | 0 0 2 0 3 1 2 0 | 0 1 3 1 . . o . . *c3x | 3 | 0 3 | * * * 8640 | 0 0 0 2 0 2 | 0 0 2 0 0 2 1 1 | 0 2 2 0 ------------------+------+-----------+----------------------+-------------------------------+--------------------------------------+-------------- x3o3o . . . & ♦ 4 | 6 0 | 4 0 0 0 | 4320 * * * * * | 1 1 1 0 0 0 0 0 | 1 1 1 0 x3o . . x . & ♦ 6 | 9 0 | 2 3 0 0 | * 8640 * * * * | 0 1 0 1 1 0 0 0 | 1 0 1 1 x3o . . . x & ♦ 6 | 6 3 | 2 0 3 0 | * * 4320 * * * | 0 0 2 0 2 0 0 0 | 0 1 2 1 x . o . . *c3x & ♦ 6 | 3 6 | 0 0 3 2 | * * * 8640 * * | 0 0 1 0 0 1 1 0 | 0 1 2 0 x . . . x x ♦ 8 | 8 4 | 0 2 4 0 | * * * * 6480 * | 0 0 0 0 2 0 1 0 | 0 0 2 1 . o3o . . *c3x & ♦ 4 | 0 6 | 0 0 0 4 | * * * * * 4320 | 0 0 1 0 0 1 0 1 | 0 2 1 0 ------------------+------+-----------+----------------------+-------------------------------+--------------------------------------+-------------- x3o3o3o . . & ♦ 5 | 10 0 | 10 0 0 0 | 5 0 0 0 0 0 | 864 * * * * * * * | 1 1 0 0 x3o3o . x . & ♦ 8 | 16 0 | 8 6 0 0 | 2 4 0 0 0 0 | * 2160 * * * * * * | 1 0 1 0 x3o3o . . *c3x & ♦ 20 | 30 30 | 20 0 30 20 | 5 0 10 10 0 5 | * * 864 * * * * * | 0 1 1 0 x3o . o3x . ♦ 9 | 18 0 | 6 9 0 0 | 0 6 0 0 0 0 | * * * 1440 * * * * | 1 0 0 1 x3o . . x x & ♦ 12 | 18 6 | 4 6 9 0 | 0 2 2 0 3 0 | * * * * 4320 * * * | 0 0 1 1 x . o3o . *c3x & ♦ 8 | 4 12 | 0 0 6 8 | 0 0 0 4 0 2 | * * * * * 2160 * * | 0 1 1 0 x . o . x *c3x ♦ 12 | 12 12 | 0 3 12 4 | 0 0 0 4 3 0 | * * * * * * 2160 * | 0 0 2 0 . o3o3o . *c3x ♦ 8 | 0 24 | 0 0 0 32 | 0 0 0 0 0 16 | * * * * * * * 270 | 0 2 0 0 ------------------+------+-----------+----------------------+-------------------------------+--------------------------------------+-------------- x3o3o3o3x . ♦ 30 | 120 0 | 120 90 0 0 | 60 120 0 0 0 0 | 12 30 0 20 0 0 0 0 | 72 * * * x3o3o3o . *c3x & ♦ 80 | 160 240 | 160 0 240 320 | 80 0 80 160 0 160 | 16 0 16 0 0 40 0 10 | * 54 * * x3o3o . x *c3x & ♦ 40 | 80 60 | 40 30 90 40 | 10 20 20 40 30 10 | 0 5 2 0 10 5 10 0 | * * 432 * x3o . o3x x ♦ 18 | 36 9 | 12 18 18 0 | 0 12 6 0 9 0 | 0 0 0 2 6 0 0 0 | * * * 720
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