©
©
| by facets: | qrit | quithip | quitit | rap | tepe | tistodip | wavitoth |
| quarn | 10 | 0 | 0 | 32 | 80 | 0 | 0 |
| gafwan | 0 | 40 | 10 | 0 | 80 | 80 | 0 |
| wavinant | 0 | 0 | 10 | 32 | 0 | 0 | 10 |
- general polytopal classes:
- Wythoffian polytera
links
| Acronym | wavinant | ||||||||||||||||||||||||||||||||
| Name | sphenoverted penteractipenteractitriacontaditeron | ||||||||||||||||||||||||||||||||
| Field of sections |
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| Circumradius | sqrt[11-6 sqrt(2)]/2 = 0.792893 | ||||||||||||||||||||||||||||||||
| Vertex figure |
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| Coordinates | (sqrt(2)-1, sqrt(2)-1, sqrt(2)-1, 1, 1)/2 & all permutations, all changes of sign | ||||||||||||||||||||||||||||||||
| Colonel of regiment |
(is itself locally convex
– other uniform polyteral members:
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| Face vector | 320, 1280, 1280, 440, 52 | ||||||||||||||||||||||||||||||||
| Confer |
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External links |
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As abstract polytope wavinant is isomorphic to rawn, thereby replacing octagrams by octagons, resp. quith by tic and gocco by socco, resp. quitit by tat and wavitoth by rawvatoth.
Incidence matrix according to Dynkin symbol
3 3 3
o---x---o---o
4 \ / 4/3
x
o3o3x3o4x4/3*c . . . . . | 320 | 6 2 | 6 3 6 1 | 2 3 6 3 | 1 2 3 ---------------+-----+---------+----------------+---------------+--------- . . x . . | 2 | 960 * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . . x | 2 | * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 ---------------+-----+---------+----------------+---------------+--------- . o3x . . | 3 | 3 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3o . | 3 | 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x4/3*c | 8 | 4 4 | * * 240 * | 0 0 2 1 | 0 1 2 . . . o4x | 4 | 0 4 | * * * 80 | 0 0 0 3 | 0 0 3 ---------------+-----+---------+----------------+---------------+--------- o3o3x . . ♦ 4 | 6 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3x3o . ♦ 6 | 12 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3x . x4/3*c ♦ 24 | 24 12 | 8 0 6 0 | * * 80 * | 0 1 1 . . x3o4x4/3*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 40 | 0 0 2 ---------------+-----+---------+----------------+---------------+--------- o3o3x3o . ♦ 10 | 30 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3o3x . x4/3*c ♦ 64 | 96 32 | 64 0 24 0 | 16 0 8 0 | * 10 * . o3x3o4x4/3*c ♦ 96 | 192 96 | 64 64 48 24 | 0 16 8 8 | * * 10
3/2 3 3
o---x---o---o
4/3 \ / 4/3
x
o3o3x3/2o4/3x4/3*c . . . . . | 320 | 6 2 | 6 3 6 1 | 2 3 6 3 | 1 2 3 -------------------+-----+---------+----------------+---------------+--------- . . x . . | 2 | 960 * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . . x | 2 | * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 -------------------+-----+---------+----------------+---------------+--------- . o3x . . | 3 | 3 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3/2o . | 3 | 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x4/3*c | 8 | 4 4 | * * 240 * | 0 0 2 1 | 0 1 2 . . . o4/3x | 4 | 0 4 | * * * 80 | 0 0 0 3 | 0 0 3 -------------------+-----+---------+----------------+---------------+--------- o3o3x . . ♦ 4 | 6 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3x3/2o . ♦ 6 | 12 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3x . x4/3*c ♦ 24 | 24 12 | 8 0 6 0 | * * 80 * | 0 1 1 . . x3/2o4/3x4/3*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 40 | 0 0 2 -------------------+-----+---------+----------------+---------------+--------- o3o3x3/2o . ♦ 10 | 30 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3o3x . x4/3*c ♦ 64 | 96 32 | 64 0 24 0 | 16 0 8 0 | * 10 * . o3x3/2o4/3x4/3*c ♦ 96 | 192 96 | 64 64 48 24 | 0 16 8 8 | * * 10
3 3 3/2
o---x---o---o
4 \ / 4/3
x
o3/2o3x3o4x4/3*c . . . . . | 320 | 6 2 | 6 3 6 1 | 2 3 6 3 | 1 2 3 -----------------+-----+---------+----------------+---------------+--------- . . x . . | 2 | 960 * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . . x | 2 | * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 -----------------+-----+---------+----------------+---------------+--------- . o3x . . | 3 | 3 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3o . | 3 | 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x4/3*c | 8 | 4 4 | * * 240 * | 0 0 2 1 | 0 1 2 . . . o4x | 4 | 0 4 | * * * 80 | 0 0 0 3 | 0 0 3 -----------------+-----+---------+----------------+---------------+--------- o3/2o3x . . ♦ 4 | 6 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3x3o . ♦ 6 | 12 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3x . x4/3*c ♦ 24 | 24 12 | 8 0 6 0 | * * 80 * | 0 1 1 . . x3o4x4/3*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 40 | 0 0 2 -----------------+-----+---------+----------------+---------------+--------- o3/2o3x3o . ♦ 10 | 30 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3/2o3x . x4/3*c ♦ 64 | 96 32 | 64 0 24 0 | 16 0 8 0 | * 10 * . o3x3o4x4/3*c ♦ 96 | 192 96 | 64 64 48 24 | 0 16 8 8 | * * 10
3/2 3 3/2
o---x---o---o
4/3 \ / 4/3
x
o3/2o3x3/2o4/3x4/3*c . . . . . | 320 | 6 2 | 6 3 6 1 | 2 3 6 3 | 1 2 3 ---------------------+-----+---------+----------------+---------------+--------- . . x . . | 2 | 960 * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . . x | 2 | * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 ---------------------+-----+---------+----------------+---------------+--------- . o3x . . | 3 | 3 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3/2o . | 3 | 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x4/3*c | 8 | 4 4 | * * 240 * | 0 0 2 1 | 0 1 2 . . . o4/3x | 4 | 0 4 | * * * 80 | 0 0 0 3 | 0 0 3 ---------------------+-----+---------+----------------+---------------+--------- o3/2o3x . . ♦ 4 | 6 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3x3/2o . ♦ 6 | 12 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3x . x4/3*c ♦ 24 | 24 12 | 8 0 6 0 | * * 80 * | 0 1 1 . . x3/2o4/3x4/3*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 40 | 0 0 2 ---------------------+-----+---------+----------------+---------------+--------- o3/2o3x3/2o . ♦ 10 | 30 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3/2o3x . x4/3*c ♦ 64 | 96 32 | 64 0 24 0 | 16 0 8 0 | * 10 * . o3x3/2o4/3x4/3*c ♦ 96 | 192 96 | 64 64 48 24 | 0 16 8 8 | * * 10
3 3/2 3
o---x---o---o
4 \ / 4/3
x
o3o3/2x3o4x4/3*c . . . . . | 320 | 6 2 | 6 3 6 1 | 2 3 6 3 | 1 2 3 -----------------+-----+---------+----------------+---------------+--------- . . x . . | 2 | 960 * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . . x | 2 | * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 -----------------+-----+---------+----------------+---------------+--------- . o3/2x . . | 3 | 3 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3o . | 3 | 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x4/3*c | 8 | 4 4 | * * 240 * | 0 0 2 1 | 0 1 2 . . . o4x | 4 | 0 4 | * * * 80 | 0 0 0 3 | 0 0 3 -----------------+-----+---------+----------------+---------------+--------- o3o3/2x . . ♦ 4 | 6 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3/2x3o . ♦ 6 | 12 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3/2x . x4/3*c ♦ 24 | 24 12 | 8 0 6 0 | * * 80 * | 0 1 1 . . x3o4x4/3*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 40 | 0 0 2 -----------------+-----+---------+----------------+---------------+--------- o3o3/2x3o . ♦ 10 | 30 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3o3/2x . x4/3*c ♦ 64 | 96 32 | 64 0 24 0 | 16 0 8 0 | * 10 * . o3/2x3o4x4/3*c ♦ 96 | 192 96 | 64 64 48 24 | 0 16 8 8 | * * 10
3/2 3/2 3
o---x---o---o
4/3 \ / 4/3
x
o3o3/2x3/2o4/3x4/3*c . . . . . | 320 | 6 2 | 6 3 6 1 | 2 3 6 3 | 1 2 3 ---------------------+-----+---------+----------------+---------------+--------- . . x . . | 2 | 960 * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . . x | 2 | * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 ---------------------+-----+---------+----------------+---------------+--------- . o3/2x . . | 3 | 3 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3/2o . | 3 | 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x4/3*c | 8 | 4 4 | * * 240 * | 0 0 2 1 | 0 1 2 . . . o4/3x | 4 | 0 4 | * * * 80 | 0 0 0 3 | 0 0 3 ---------------------+-----+---------+----------------+---------------+--------- o3o3/2x . . ♦ 4 | 6 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3/2x3/2o . ♦ 6 | 12 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3/2x . x4/3*c ♦ 24 | 24 12 | 8 0 6 0 | * * 80 * | 0 1 1 . . x3/2o4/3x4/3*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 40 | 0 0 2 ---------------------+-----+---------+----------------+---------------+--------- o3o3/2x3/2o . ♦ 10 | 30 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3o3/2x . x4/3*c ♦ 64 | 96 32 | 64 0 24 0 | 16 0 8 0 | * 10 * . o3/2x3/2o4/3x4/3*c ♦ 96 | 192 96 | 64 64 48 24 | 0 16 8 8 | * * 10
3 3/2 3/2
o---x---o---o
4 \ / 4/3
x
o3/2o3/2x3o4x4/3*c . . . . . | 320 | 6 2 | 6 3 6 1 | 2 3 6 3 | 1 2 3 -------------------+-----+---------+----------------+---------------+--------- . . x . . | 2 | 960 * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . . x | 2 | * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 -------------------+-----+---------+----------------+---------------+--------- . o3/2x . . | 3 | 3 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3o . | 3 | 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x4/3*c | 8 | 4 4 | * * 240 * | 0 0 2 1 | 0 1 2 . . . o4x | 4 | 0 4 | * * * 80 | 0 0 0 3 | 0 0 3 -------------------+-----+---------+----------------+---------------+--------- o3/2o3/2x . . ♦ 4 | 6 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3/2x3o . ♦ 6 | 12 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3/2x . x4/3*c ♦ 24 | 24 12 | 8 0 6 0 | * * 80 * | 0 1 1 . . x3o4x4/3*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 40 | 0 0 2 -------------------+-----+---------+----------------+---------------+--------- o3/2o3/2x3o . ♦ 10 | 30 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3/2o3/2x . x4/3*c ♦ 64 | 96 32 | 64 0 24 0 | 16 0 8 0 | * 10 * . o3x3/2o4x4/3*c ♦ 96 | 192 96 | 64 64 48 24 | 0 16 8 8 | * * 10
3/2 3/2 3/2
o---x---o---o
4/3 \ / 4/3
x
o3/2o3/2x3/2o4/3x4/3*c . . . . . | 320 | 6 2 | 6 3 6 1 | 2 3 6 3 | 1 2 3 -----------------------+-----+---------+----------------+---------------+--------- . . x . . | 2 | 960 * | 2 1 1 0 | 1 2 2 1 | 1 1 2 . . . . x | 2 | * 320 | 0 0 3 1 | 0 0 3 3 | 0 1 3 -----------------------+-----+---------+----------------+---------------+--------- . o3/2x . . | 3 | 3 0 | 640 * * * | 1 1 1 0 | 1 1 1 . . x3/2o . | 3 | 3 0 | * 320 * * | 0 2 0 1 | 1 0 2 . . x . x4/3*c | 8 | 4 4 | * * 240 * | 0 0 2 1 | 0 1 2 . . . o4/3x | 4 | 0 4 | * * * 80 | 0 0 0 3 | 0 0 3 -----------------------+-----+---------+----------------+---------------+--------- o3/2o3/2x . . ♦ 4 | 6 0 | 4 0 0 0 | 160 * * * | 1 1 0 . o3/2x3/2o . ♦ 6 | 12 0 | 4 4 0 0 | * 160 * * | 1 0 1 . o3/2x . x4/3*c ♦ 24 | 24 12 | 8 0 6 0 | * * 80 * | 0 1 1 . . x3/2o4/3x4/3*c ♦ 24 | 24 24 | 0 8 6 6 | * * * 40 | 0 0 2 -----------------------+-----+---------+----------------+---------------+--------- o3/2o3/2x3/2o . ♦ 10 | 30 0 | 20 10 0 0 | 5 5 0 0 | 32 * * o3/2o3/2x . x4/3*c ♦ 64 | 96 32 | 64 0 24 0 | 16 0 8 0 | * 10 * . o3/2x3/2o4/3x4/3*c ♦ 96 | 192 96 | 64 64 48 24 | 0 16 8 8 | * * 10
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