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- general polytopal classes:
- Wythoffian polytera
links
| Acronym | nottant |
| Name | penteractitruncated penteractitriacontaditeron |
| Field of sections |
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| Circumradius | sqrt[13+4 sqrt(2)]/2 = 2.159679 |
| Vertex figure |
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| Coordinates | ((1+sqrt(2))/2, (1+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 | 640, 1600, 1280, 440, 52 |
| Confer |
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External links |
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As abstract polytope nottant is isomorphic to naquitant, thereby interchanging the roles of octagrams and octagons, resp. replacing tic by quith, resp. tat by quitit, and thatoth by thaquitoth.
Incidence matrix according to Dynkin symbol
3 3 3
o---o---x---x
4 \ / 4/3
x
o3o3x3x4/3x4*c . . . . . | 640 | 3 1 1 | 3 3 3 1 | 1 3 3 3 | 1 1 3 ---------------+-----+-------------+----------------+---------------+--------- . . x . . | 2 | 960 * * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . x . | 2 | * 320 * | 0 3 0 1 | 0 3 0 3 | 1 0 3 . . . . x | 2 | * * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 ---------------+-----+-------------+----------------+---------------+--------- . o3x . . | 3 | 3 0 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3x . | 6 | 3 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x4*c | 8 | 4 0 4 | * * 240 * | 0 0 2 1 | 0 1 2 . . . x4/3x | 8 | 0 4 4 | * * * 80 | 0 0 0 3 | 0 0 3 ---------------+-----+-------------+----------------+---------------+--------- o3o3x . . ♦ 4 | 6 0 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3x3x . ♦ 12 | 12 6 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3x . x4*c ♦ 24 | 24 0 12 | 8 0 6 0 | * * 80 * | 0 1 1 . . x3x4/3x4*c ♦ 48 | 24 24 24 | 0 8 6 6 | * * * 40 | 0 0 2 ---------------+-----+-------------+----------------+---------------+--------- o3o3x3x . ♦ 20 | 30 10 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3o3x . x4*c ♦ 64 | 96 0 32 | 64 0 24 0 | 16 0 8 0 | * 10 * . o3x3x4/3x4*c ♦ 192 | 192 96 96 | 64 64 48 24 | 0 16 8 8 | * * 10
3/2 3 3
o---o---x---x
4 \ / 4/3
x
o3/2o3x3x4/3x4*c . . . . . | 640 | 3 1 1 | 3 3 3 1 | 1 3 3 3 | 1 1 3 -----------------+-----+-------------+----------------+---------------+--------- . . x . . | 2 | 960 * * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . x . | 2 | * 320 * | 0 3 0 1 | 0 3 0 3 | 1 0 3 . . . . x | 2 | * * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 -----------------+-----+-------------+----------------+---------------+--------- . o3x . . | 3 | 3 0 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3x . | 6 | 3 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x4*c | 8 | 4 0 4 | * * 240 * | 0 0 2 1 | 0 1 2 . . . x4/3x | 8 | 0 4 4 | * * * 80 | 0 0 0 3 | 0 0 3 -----------------+-----+-------------+----------------+---------------+--------- o3/2o3x . . ♦ 4 | 6 0 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3x3x . ♦ 12 | 12 6 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3x . x4*c ♦ 24 | 24 0 12 | 8 0 6 0 | * * 80 * | 0 1 1 . . x3x4/3x4*c ♦ 48 | 24 24 24 | 0 8 6 6 | * * * 40 | 0 0 2 -----------------+-----+-------------+----------------+---------------+--------- o3/2o3x3x . ♦ 20 | 30 10 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3/2o3x . x4*c ♦ 64 | 96 0 32 | 64 0 24 0 | 16 0 8 0 | * 10 * . o3x3x4/3x4*c ♦ 192 | 192 96 96 | 64 64 48 24 | 0 16 8 8 | * * 10
3 3/2 3
o---o---x---x
4 \ / 4/3
x
o3o3/2x3x4/3x4*c . . . . . | 640 | 3 1 1 | 3 3 3 1 | 1 3 3 3 | 1 1 3 -----------------+-----+-------------+----------------+---------------+--------- . . x . . | 2 | 960 * * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . x . | 2 | * 320 * | 0 3 0 1 | 0 3 0 3 | 1 0 3 . . . . x | 2 | * * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 -----------------+-----+-------------+----------------+---------------+--------- . o3/2x . . | 3 | 3 0 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3x . | 6 | 3 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x4*c | 8 | 4 0 4 | * * 240 * | 0 0 2 1 | 0 1 2 . . . x4/3x | 8 | 0 4 4 | * * * 80 | 0 0 0 3 | 0 0 3 -----------------+-----+-------------+----------------+---------------+--------- o3o3/2x . . ♦ 4 | 6 0 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3/2x3x . ♦ 12 | 12 6 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3/2x . x4*c ♦ 24 | 24 0 12 | 8 0 6 0 | * * 80 * | 0 1 1 . . x3x4/3x4*c ♦ 48 | 24 24 24 | 0 8 6 6 | * * * 40 | 0 0 2 -----------------+-----+-------------+----------------+---------------+--------- o3o3/2x3x . ♦ 20 | 30 10 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3o3/2x . x4*c ♦ 64 | 96 0 32 | 64 0 24 0 | 16 0 8 0 | * 10 * . o3/2x3x4/3x4*c ♦ 192 | 192 96 96 | 64 64 48 24 | 0 16 8 8 | * * 10
3/2 3/2 3
o---o---x---x
4 \ / 4/3
x
o3/2o3/2x3x4/3x4*c . . . . . | 640 | 3 1 1 | 3 3 3 1 | 1 3 3 3 | 1 1 3 -------------------+-----+-------------+----------------+---------------+--------- . . x . . | 2 | 960 * * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . x . | 2 | * 320 * | 0 3 0 1 | 0 3 0 3 | 1 0 3 . . . . x | 2 | * * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 -------------------+-----+-------------+----------------+---------------+--------- . o3/2x . . | 3 | 3 0 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3x . | 6 | 3 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x4*c | 8 | 4 0 4 | * * 240 * | 0 0 2 1 | 0 1 2 . . . x4/3x | 8 | 0 4 4 | * * * 80 | 0 0 0 3 | 0 0 3 -------------------+-----+-------------+----------------+---------------+--------- o3/2o3/2x . . ♦ 4 | 6 0 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3/2x3x . ♦ 12 | 12 6 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3/2x . x4*c ♦ 24 | 24 0 12 | 8 0 6 0 | * * 80 * | 0 1 1 . . x3x4/3x4*c ♦ 48 | 24 24 24 | 0 8 6 6 | * * * 40 | 0 0 2 -------------------+-----+-------------+----------------+---------------+--------- o3/2o3/2x3x . ♦ 20 | 30 10 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3/2o3/2x . x4*c ♦ 64 | 96 0 32 | 64 0 24 0 | 16 0 8 0 | * 10 * . o3/2x3x4/3x4*c ♦ 192 | 192 96 96 | 64 64 48 24 | 0 16 8 8 | * * 10
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