omnitruncated hemipenteract
©
wrt. shiddip
wrt. tope
wrt. gippid
wrt. tico
©
©
- general polytopal classes:
- Wythoffian polytera lace simplices partial Stott expansions
- analogs:
- omnitruncated Gossetic ot(n2,1)
links
| Acronym | gippit |
| Name |
great prismated triacontiditeron, omnitruncated hemipenteract |
| Field of sections |
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| Circumradius | sqrt(15) = 3.872983 |
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Inradius wrt. shiddip | sqrt(27/2) = 3.674235 |
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Inradius wrt. tope | 7/2 = 3.5 |
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Inradius wrt. gippid | sqrt(10) = 3.162278 |
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Inradius wrt. tico | sqrt(8) = 2.828427 |
| Vertex figure |
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| Coordinates | (4, 3, 2, 1, 0)/sqrt(2) & all permutations, all changes of sign |
| Face vector | 1920, 4800, 4160, 1440, 162 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3x3x3x4o . . . . . | 1920 | 1 1 1 2 | 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 | 2 1 1 1 ----------+------+------------------+-----------------------------+---------------------------+------------ x . . . . | 2 | 960 * * * | 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0 . x . . . | 2 | * 960 * * | 1 0 0 1 2 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1 . . x . . | 2 | * * 960 * | 0 1 0 1 0 2 0 | 1 0 2 0 2 0 1 | 2 0 1 1 . . . x . | 2 | * * * 1920 | 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1 ----------+------+------------------+-----------------------------+---------------------------+------------ x3x . . . | 6 | 3 3 0 0 | 320 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0 x . x . . | 4 | 2 0 2 0 | * 480 * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0 x . . x . | 4 | 2 0 0 2 | * * 960 * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 . x3x . . | 6 | 0 3 3 0 | * * * 320 * * * | 1 0 0 0 2 0 0 | 2 0 0 1 . x . x . | 4 | 0 2 0 2 | * * * * 960 * * | 0 1 0 0 1 1 0 | 1 1 0 1 . . x3x . | 6 | 0 0 3 3 | * * * * * 640 * | 0 0 1 0 1 0 1 | 1 0 1 1 . . . x4o | 4 | 0 0 0 4 | * * * * * * 480 | 0 0 0 1 0 1 1 | 0 1 1 1 ----------+------+------------------+-----------------------------+---------------------------+------------ x3x3x . . ♦ 24 | 12 12 12 0 | 4 6 0 4 0 0 0 | 80 * * * * * * | 2 0 0 0 x3x . x . ♦ 12 | 6 6 0 6 | 2 0 3 0 3 0 0 | * 320 * * * * * | 1 1 0 0 x . x3x . ♦ 12 | 6 0 6 6 | 0 3 3 0 0 2 0 | * * 320 * * * * | 1 0 1 0 x . . x4o ♦ 8 | 4 0 0 8 | 0 0 4 0 0 0 2 | * * * 240 * * * | 0 1 1 0 . x3x3x . ♦ 24 | 0 12 12 12 | 0 0 0 4 6 4 0 | * * * * 160 * * | 1 0 0 1 . x . x4o ♦ 8 | 0 4 0 8 | 0 0 0 0 4 0 2 | * * * * * 240 * | 0 1 0 1 . . x3x4o ♦ 24 | 0 0 12 24 | 0 0 0 0 0 8 6 | * * * * * * 80 | 0 0 1 1 ----------+------+------------------+-----------------------------+---------------------------+------------ x3x3x3x . ♦ 120 | 60 60 60 60 | 20 30 30 20 30 20 0 | 5 10 10 0 5 0 0 | 32 * * * x3x . x4o ♦ 24 | 12 12 0 24 | 4 0 12 0 12 0 6 | 0 4 0 3 0 3 0 | * 80 * * x . x3x4o ♦ 48 | 24 0 24 48 | 0 12 24 0 0 16 12 | 0 0 8 6 0 0 2 | * * 40 * . x3x3x4o ♦ 192 | 0 96 96 192 | 0 0 0 32 96 64 48 | 0 0 0 0 16 24 8 | * * * 10 snubbed forms: s3s3s3s4o
x3x3x3x4/3o . . . . . | 1920 | 1 1 1 2 | 1 1 2 1 2 2 1 | 1 2 2 1 2 1 1 | 2 1 1 1 ------------+------+------------------+-----------------------------+---------------------------+------------ x . . . . | 2 | 960 * * * | 1 1 2 0 0 0 0 | 1 2 2 1 0 0 0 | 2 1 1 0 . x . . . | 2 | * 960 * * | 1 0 0 1 2 0 0 | 1 2 0 0 2 1 0 | 2 1 0 1 . . x . . | 2 | * * 960 * | 0 1 0 1 0 2 0 | 1 0 2 0 2 0 1 | 2 0 1 1 . . . x . | 2 | * * * 1920 | 0 0 1 0 1 1 1 | 0 1 1 1 1 1 1 | 1 1 1 1 ------------+------+------------------+-----------------------------+---------------------------+------------ x3x . . . | 6 | 3 3 0 0 | 320 * * * * * * | 1 2 0 0 0 0 0 | 2 1 0 0 x . x . . | 4 | 2 0 2 0 | * 480 * * * * * | 1 0 2 0 0 0 0 | 2 0 1 0 x . . x . | 4 | 2 0 0 2 | * * 960 * * * * | 0 1 1 1 0 0 0 | 1 1 1 0 . x3x . . | 6 | 0 3 3 0 | * * * 320 * * * | 1 0 0 0 2 0 0 | 2 0 0 1 . x . x . | 4 | 0 2 0 2 | * * * * 960 * * | 0 1 0 0 1 1 0 | 1 1 0 1 . . x3x . | 6 | 0 0 3 3 | * * * * * 640 * | 0 0 1 0 1 0 1 | 1 0 1 1 . . . x4/3o | 4 | 0 0 0 4 | * * * * * * 480 | 0 0 0 1 0 1 1 | 0 1 1 1 ------------+------+------------------+-----------------------------+---------------------------+------------ x3x3x . . ♦ 24 | 12 12 12 0 | 4 6 0 4 0 0 0 | 80 * * * * * * | 2 0 0 0 x3x . x . ♦ 12 | 6 6 0 6 | 2 0 3 0 3 0 0 | * 320 * * * * * | 1 1 0 0 x . x3x . ♦ 12 | 6 0 6 6 | 0 3 3 0 0 2 0 | * * 320 * * * * | 1 0 1 0 x . . x4/3o ♦ 8 | 4 0 0 8 | 0 0 4 0 0 0 2 | * * * 240 * * * | 0 1 1 0 . x3x3x . ♦ 24 | 0 12 12 12 | 0 0 0 4 6 4 0 | * * * * 160 * * | 1 0 0 1 . x . x4/3o ♦ 8 | 0 4 0 8 | 0 0 0 0 4 0 2 | * * * * * 240 * | 0 1 0 1 . . x3x4/3o ♦ 24 | 0 0 12 24 | 0 0 0 0 0 8 6 | * * * * * * 80 | 0 0 1 1 ------------+------+------------------+-----------------------------+---------------------------+------------ x3x3x3x . ♦ 120 | 60 60 60 60 | 20 30 30 20 30 20 0 | 5 10 10 0 5 0 0 | 32 * * * x3x . x4/3o ♦ 24 | 12 12 0 24 | 4 0 12 0 12 0 6 | 0 4 0 3 0 3 0 | * 80 * * x . x3x4/3o ♦ 48 | 24 0 24 48 | 0 12 24 0 0 16 12 | 0 0 8 6 0 0 2 | * * 40 * . x3x3x4/3o ♦ 192 | 0 96 96 192 | 0 0 0 32 96 64 48 | 0 0 0 0 16 24 8 | * * * 10
x
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x---x---x
3 / 3 3
x
x3x3x *b3x3x . . . . . | 1920 | 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 -------------+------+---------------------+-----------------------------------------+-------------------------------------+--------------- x . . . . | 2 | 960 * * * * | 1 1 1 1 0 0 0 0 0 0 | 1 1 1 1 1 1 0 0 0 0 | 1 1 1 1 0 . x . . . | 2 | * 960 * * * | 1 0 0 0 1 1 1 0 0 0 | 1 1 1 0 0 0 1 1 1 0 | 1 1 1 0 1 . . x . . | 2 | * * 960 * * | 0 1 0 0 1 0 0 1 1 0 | 1 0 0 1 1 0 1 1 0 1 | 1 1 0 1 1 . . . x . | 2 | * * * 960 * | 0 0 1 0 0 1 0 1 0 1 | 0 1 0 1 0 1 1 0 1 1 | 1 0 1 1 1 . . . . x | 2 | * * * * 960 | 0 0 0 1 0 0 1 0 1 1 | 0 0 1 0 1 1 0 1 1 1 | 0 1 1 1 1 -------------+------+---------------------+-----------------------------------------+-------------------------------------+--------------- x3x . . . | 6 | 3 3 0 0 0 | 320 * * * * * * * * * | 1 1 1 0 0 0 0 0 0 0 | 1 1 1 0 0 x . x . . | 4 | 2 0 2 0 0 | * 480 * * * * * * * * | 1 0 0 1 1 0 0 0 0 0 | 1 1 0 1 0 x . . x . | 4 | 2 0 0 2 0 | * * 480 * * * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 0 1 1 0 x . . . x | 4 | 2 0 0 0 2 | * * * 480 * * * * * * | 0 0 1 0 1 1 0 0 0 0 | 0 1 1 1 0 . x3x . . | 6 | 0 3 3 0 0 | * * * * 320 * * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x . *b3x . | 6 | 0 3 0 3 0 | * * * * * 320 * * * * | 0 1 0 0 0 0 1 0 1 0 | 1 0 1 0 1 . x . . x | 4 | 0 2 0 0 2 | * * * * * * 480 * * * | 0 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1 . . x x . | 4 | 0 0 2 2 0 | * * * * * * * 480 * * | 0 0 0 1 0 0 1 0 0 1 | 1 0 0 1 1 . . x . x | 4 | 0 0 2 0 2 | * * * * * * * * 480 * | 0 0 0 0 1 0 0 1 0 1 | 0 1 0 1 1 . . . x3x | 6 | 0 0 0 3 3 | * * * * * * * * * 320 | 0 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1 -------------+------+---------------------+-----------------------------------------+-------------------------------------+--------------- x3x3x . . ♦ 24 | 12 12 12 0 0 | 4 6 0 0 4 0 0 0 0 0 | 80 * * * * * * * * * | 1 1 0 0 0 x3x . *b3x . ♦ 24 | 12 12 0 12 0 | 4 0 6 0 0 4 0 0 0 0 | * 80 * * * * * * * * | 1 0 1 0 0 x3x . . x ♦ 12 | 6 6 0 0 6 | 2 0 0 3 0 0 3 0 0 0 | * * 160 * * * * * * * | 0 1 1 0 0 x . x x . ♦ 8 | 4 0 4 4 0 | 0 2 2 0 0 0 0 2 0 0 | * * * 240 * * * * * * | 1 0 0 1 0 x . x . x ♦ 8 | 4 0 4 0 4 | 0 2 0 2 0 0 0 0 2 0 | * * * * 240 * * * * * | 0 1 0 1 0 x . . x3x ♦ 12 | 6 0 0 6 6 | 0 0 3 3 0 0 0 0 0 2 | * * * * * 160 * * * * | 0 0 1 1 0 . x3x *b3x . ♦ 24 | 0 12 12 12 0 | 0 0 0 0 4 4 0 6 0 0 | * * * * * * 80 * * * | 1 0 0 0 1 . x3x . x ♦ 12 | 0 6 6 0 6 | 0 0 0 0 2 0 3 0 3 0 | * * * * * * * 160 * * | 0 1 0 0 1 . x . *b3x3x ♦ 24 | 0 12 0 12 12 | 0 0 0 0 0 4 6 0 0 4 | * * * * * * * * 80 * | 0 0 1 0 1 . . x x3x ♦ 12 | 0 0 6 6 6 | 0 0 0 0 0 0 0 3 3 2 | * * * * * * * * * 160 | 0 0 0 1 1 -------------+------+---------------------+-----------------------------------------+-------------------------------------+--------------- x3x3x *b3x . ♦ 192 | 96 96 96 96 0 | 32 48 48 0 32 32 0 48 0 0 | 8 8 0 24 0 0 8 0 0 0 | 10 * * * * x3x3x . x ♦ 48 | 24 24 24 0 24 | 8 12 0 12 8 0 12 0 12 0 | 2 0 4 0 6 0 0 4 0 0 | * 40 * * * x3x . *b3x3x ♦ 120 | 60 60 0 60 60 | 20 0 30 30 0 20 30 0 0 20 | 0 5 10 0 0 10 0 0 5 0 | * * 16 * * x . x x3x ♦ 24 | 12 0 12 12 12 | 0 6 6 6 0 0 0 6 6 4 | 0 0 0 3 3 2 0 0 0 2 | * * * 80 * . x3x *b3x3x ♦ 120 | 0 60 60 60 60 | 0 0 0 0 20 20 30 30 30 20 | 0 0 0 0 0 0 5 10 5 10 | * * * * 16 snubbed forms: s3s3s *b3s3s
x3x3x3x4s
demi( . . . . . ) | 1920 | 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1
------------------+------+---------------------+-----------------------------------------+-------------------------------------+---------------
demi( x . . . . ) | 2 | 960 * * * * | 1 1 1 0 0 0 0 1 0 0 | 1 1 1 0 1 0 0 1 1 0 | 1 1 1 0 1
demi( . x . . . ) | 2 | * 960 * * * | 1 0 0 1 1 0 0 0 1 0 | 1 1 0 1 0 1 0 1 0 1 | 1 1 0 1 1
demi( . . x . . ) | 2 | * * 960 * * | 0 1 0 1 0 1 0 0 0 1 | 1 0 1 1 0 0 1 0 1 1 | 1 0 1 1 1
demi( . . . x . ) | 2 | * * * 960 * | 0 0 1 0 1 1 1 0 0 0 | 0 1 1 1 1 1 1 0 0 0 | 1 1 1 1 0
sefa( . . . x4s ) | 2 | * * * * 960 | 0 0 0 0 0 0 1 1 1 1 | 0 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1
------------------+------+---------------------+-----------------------------------------+-------------------------------------+---------------
demi( x3x . . . ) | 6 | 3 3 0 0 0 | 320 * * * * * * * * * | 1 1 0 0 0 0 0 1 0 0 | 1 1 0 0 1
demi( x . x . . ) | 4 | 2 0 2 0 0 | * 480 * * * * * * * * | 1 0 1 0 0 0 0 0 1 0 | 1 0 1 0 1
demi( x . . x . ) | 4 | 2 0 0 2 0 | * * 480 * * * * * * * | 0 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
demi( . x3x . . ) | 6 | 0 3 3 0 0 | * * * 320 * * * * * * | 1 0 0 1 0 0 0 0 0 1 | 1 0 0 1 1
demi( . x . x . ) | 4 | 0 2 0 2 0 | * * * * 480 * * * * * | 0 1 0 1 0 1 0 0 0 0 | 1 1 0 1 0
demi( . . x3x . ) | 6 | 0 0 3 3 0 | * * * * * 320 * * * * | 0 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
. . . x4s | 4 | 0 0 0 2 2 | * * * * * * 480 * * * | 0 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0
sefa( x 2 . x4s ) | 4 | 2 0 0 0 2 | * * * * * * * 480 * * | 0 0 0 0 1 0 0 1 1 0 | 0 1 1 0 1
sefa( . x 2 x4s ) | 4 | 0 2 0 0 2 | * * * * * * * * 480 * | 0 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1
sefa( . . x3x4s ) | 6 | 0 0 3 0 3 | * * * * * * * * * 320 | 0 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1
------------------+------+---------------------+-----------------------------------------+-------------------------------------+---------------
demi( x3x3x . . ) ♦ 24 | 12 12 12 0 0 | 4 6 0 4 0 0 0 0 0 0 | 80 * * * * * * * * * | 1 0 0 0 1
demi( x3x . x . ) ♦ 12 | 6 6 0 6 0 | 2 0 3 0 3 0 0 0 0 0 | * 160 * * * * * * * * | 1 1 0 0 0
demi( x . x3x . ) ♦ 12 | 6 0 6 6 0 | 0 3 3 0 0 2 0 0 0 0 | * * 160 * * * * * * * | 1 0 1 0 0
demi( . x3x3x . ) ♦ 24 | 0 12 12 12 0 | 0 0 0 4 6 4 0 0 0 0 | * * * 80 * * * * * * | 1 0 0 1 0
x 2 . x4s ♦ 8 | 4 0 0 4 4 | 0 0 2 0 0 0 2 2 0 0 | * * * * 240 * * * * * | 0 1 1 0 0
. x 2 x4s ♦ 8 | 0 4 0 4 4 | 0 0 0 0 2 0 2 0 2 0 | * * * * * 240 * * * * | 0 1 0 1 0
. . x3x4s ♦ 24 | 0 0 12 12 12 | 0 0 0 0 0 4 6 0 0 4 | * * * * * * 80 * * * | 0 0 1 1 0
sefa( x3x 2 x4s ) ♦ 12 | 6 6 0 0 6 | 2 0 0 0 0 0 0 3 3 0 | * * * * * * * 160 * * | 0 1 0 0 1
sefa( x 2 x3x4s ) ♦ 12 | 6 0 6 0 6 | 0 3 0 0 0 0 0 3 0 2 | * * * * * * * * 160 * | 0 0 1 0 1
sefa( . x3x3x4s ) ♦ 24 | 0 12 12 0 12 | 0 0 0 4 0 0 0 0 6 4 | * * * * * * * * * 80 | 0 0 0 1 1
------------------+------+---------------------+-----------------------------------------+-------------------------------------+---------------
demi( x3x3x3x . ) ♦ 120 | 60 60 60 60 0 | 20 30 30 20 30 20 0 0 0 0 | 5 10 10 5 0 0 0 0 0 0 | 16 * * * *
x3x 2 x4s ♦ 24 | 12 12 0 12 12 | 4 0 6 0 6 0 6 6 6 0 | 0 2 0 0 3 3 0 2 0 0 | * 80 * * *
x 2 x3x4s ♦ 48 | 24 0 24 24 24 | 0 12 12 0 0 8 12 12 0 8 | 0 0 4 0 6 0 2 0 4 0 | * * 40 * *
. x3x3x4s ♦ 192 | 0 96 96 96 96 | 0 0 0 32 48 32 48 0 48 32 | 0 0 0 8 0 24 8 0 0 8 | * * * 10 *
sefa( x3x3x3x4s ) ♦ 120 | 60 60 60 0 60 | 20 30 0 20 0 0 0 30 30 20 | 5 0 0 0 0 0 0 10 10 5 | * * * * 16
starting figure: x3x3x3x4x
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