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- general polytopal classes:
- Wythoffian polytera
links
| Acronym | nurrant |
| Name | penteractirhombated penteractitriacontaditeron |
| Field of sections |
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| Circumradius | sqrt[25+8 sqrt(2)]/2 = 3.013043 |
| Vertex figure |
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| Coordinates | ((1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, (sqrt(2)-1)/2, 1/2) & all permutations, all changes of sign |
| Colonel of regiment | (is itself locally convex – no other uniform polyteral members) |
| Face vector | 1920, 4800, 4000, 1320, 132 |
| Confer |
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External links |
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As abstract polytope nurrant is isomorphic to noqrant, thereby interchanging the roles of octagrams and octagons, resp. replacing girco by quitco and stop by op, resp. grit by gaqrit, tistodip by todipand thatpath by thaquitpath.
Incidence matrix according to Dynkin symbol
3 3 3
o---x---x---x
4 \ / 4/3
x
o3x3x3x4/3x4*c . . . . . | 1920 | 2 1 1 1 | 1 2 2 2 1 1 1 | 1 1 1 2 2 2 1 | 1 1 1 2 ---------------+------+------------------+-----------------------------+---------------------------+------------ . x . . . | 2 | 1920 * * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1 . . x . . | 2 | * 960 * * | 0 2 0 0 1 1 0 | 1 0 0 2 2 0 1 | 1 1 0 2 . . . x . | 2 | * * 960 * | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2 . . . . x | 2 | * * * 960 | 0 0 0 2 0 1 1 | 0 0 1 0 2 2 1 | 0 1 1 2 ---------------+------+------------------+-----------------------------+---------------------------+------------ o3x . . . | 3 | 3 0 0 0 | 640 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 . x3x . . | 6 | 3 3 0 0 | * 640 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 . x . x . | 4 | 2 0 2 0 | * * 960 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1 . x . . x | 4 | 2 0 0 2 | * * * 960 * * * | 0 0 1 0 1 1 0 | 0 1 1 1 . . x3x . | 6 | 0 3 3 0 | * * * * 320 * * | 0 0 0 2 0 0 1 | 1 0 0 2 . . x . x4*c | 8 | 0 4 0 4 | * * * * * 240 * | 0 0 0 0 2 0 1 | 0 1 0 2 . . . x4/3x | 8 | 0 0 4 4 | * * * * * * 240 | 0 0 0 0 0 2 1 | 0 0 1 2 ---------------+------+------------------+-----------------------------+---------------------------+------------ o3x3x . . ♦ 12 | 12 6 0 0 | 4 4 0 0 0 0 0 | 160 * * * * * * | 1 1 0 0 o3x . x . ♦ 6 | 6 0 3 0 | 2 0 3 0 0 0 0 | * 320 * * * * * | 1 0 1 0 o3x . . x ♦ 6 | 6 0 0 3 | 2 0 0 3 0 0 0 | * * 320 * * * * | 0 1 1 0 . x3x3x . ♦ 24 | 12 12 12 0 | 0 4 6 0 4 0 0 | * * * 160 * * * | 1 0 0 1 . x3x . x4*c ♦ 48 | 24 24 0 24 | 0 8 0 12 0 6 0 | * * * * 80 * * | 0 1 0 1 . x . x4/3x ♦ 16 | 8 0 8 8 | 0 0 4 4 0 0 2 | * * * * * 240 * | 0 0 1 1 . . x3x4/3x4*c ♦ 48 | 0 24 24 24 | 0 0 0 0 8 6 6 | * * * * * * 40 | 0 0 0 2 ---------------+------+------------------+-----------------------------+---------------------------+------------ o3x3x3x . ♦ 60 | 60 30 30 0 | 20 20 30 0 10 0 0 | 5 10 0 5 0 0 0 | 32 * * * o3x3x . x4*c ♦ 192 | 192 96 0 96 | 64 64 0 96 0 24 0 | 16 0 32 0 8 0 0 | * 10 * * o3x . x4/3x ♦ 24 | 24 0 12 12 | 8 0 12 12 0 0 3 | 0 4 4 0 0 3 0 | * * 80 * . x3x3x4/3x4*c ♦ 384 | 192 192 192 192 | 0 64 96 96 64 48 48 | 0 0 0 16 8 24 8 | * * * 10
3/2 3 3
o---x---x---x
4 \ / 4/3
x
o3/2x3x3x4/3x4*c . . . . . | 1920 | 2 1 1 1 | 1 2 2 2 1 1 1 | 1 1 1 2 2 2 1 | 1 1 1 2 -----------------+------+------------------+-----------------------------+---------------------------+------------ . x . . . | 2 | 1920 * * * | 1 1 1 1 0 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1 . . x . . | 2 | * 960 * * | 0 2 0 0 1 1 0 | 1 0 0 2 2 0 1 | 1 1 0 2 . . . x . | 2 | * * 960 * | 0 0 2 0 1 0 1 | 0 1 0 2 0 2 1 | 1 0 1 2 . . . . x | 2 | * * * 960 | 0 0 0 2 0 1 1 | 0 0 1 0 2 2 1 | 0 1 1 2 -----------------+------+------------------+-----------------------------+---------------------------+------------ o3/2x . . . | 3 | 3 0 0 0 | 640 * * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0 . x3x . . | 6 | 3 3 0 0 | * 640 * * * * * | 1 0 0 1 1 0 0 | 1 1 0 1 . x . x . | 4 | 2 0 2 0 | * * 960 * * * * | 0 1 0 1 0 1 0 | 1 0 1 1 . x . . x | 4 | 2 0 0 2 | * * * 960 * * * | 0 0 1 0 1 1 0 | 0 1 1 1 . . x3x . | 6 | 0 3 3 0 | * * * * 320 * * | 0 0 0 2 0 0 1 | 1 0 0 2 . . x . x4*c | 8 | 0 4 0 4 | * * * * * 240 * | 0 0 0 0 2 0 1 | 0 1 0 2 . . . x4/3x | 8 | 0 0 4 4 | * * * * * * 240 | 0 0 0 0 0 2 1 | 0 0 1 2 -----------------+------+------------------+-----------------------------+---------------------------+------------ o3/2x3x . . ♦ 12 | 12 6 0 0 | 4 4 0 0 0 0 0 | 160 * * * * * * | 1 1 0 0 o3/2x . x . ♦ 6 | 6 0 3 0 | 2 0 3 0 0 0 0 | * 320 * * * * * | 1 0 1 0 o3/2x . . x ♦ 6 | 6 0 0 3 | 2 0 0 3 0 0 0 | * * 320 * * * * | 0 1 1 0 . x3x3x . ♦ 24 | 12 12 12 0 | 0 4 6 0 4 0 0 | * * * 160 * * * | 1 0 0 1 . x3x . x4*c ♦ 48 | 24 24 0 24 | 0 8 0 12 0 6 0 | * * * * 80 * * | 0 1 0 1 . x . x4/3x ♦ 16 | 8 0 8 8 | 0 0 4 4 0 0 2 | * * * * * 240 * | 0 0 1 1 . . x3x4/3x4*c ♦ 48 | 0 24 24 24 | 0 0 0 0 8 6 6 | * * * * * * 40 | 0 0 0 2 -----------------+------+------------------+-----------------------------+---------------------------+------------ o3/2x3x3x . ♦ 60 | 60 30 30 0 | 20 20 30 0 10 0 0 | 5 10 0 5 0 0 0 | 32 * * * o3/2x3x . x4*c ♦ 192 | 192 96 0 96 | 64 64 0 96 0 24 0 | 16 0 32 0 8 0 0 | * 10 * * o3/2x . x4/3x ♦ 24 | 24 0 12 12 | 8 0 12 12 0 0 3 | 0 4 4 0 0 3 0 | * * 80 * . x3x3x4/3x4*c ♦ 384 | 192 192 192 192 | 0 64 96 96 64 48 48 | 0 0 0 16 8 24 8 | * * * 10
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