steritruncated demihexeract,
penticantic hexeract
- general polytopal classes:
- Wythoffian polypeta lace simplices
links
| Acronym | cathix |
| Name |
cellitruncated hemihexeract, steritruncated demihexeract, penticantic hexeract |
| Circumradius | sqrt(27)/2 = 2.598076 |
| Coordinates | (5/sqrt(8), 3/sqrt(8), 3/sqrt(8), 3/sqrt(8), 1/sqrt(8), 1/sqrt(8)) & all permutations, all even changes of sign |
| Face vector | 1920, 9600, 16800, 12480, 3656, 296 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
x3x3o *b3o3o3x o3o3o *b3o3o3o | 1920 | 1 6 3 | 6 3 3 6 12 3 | 3 6 12 3 3 6 2 6 6 1 | 3 6 2 6 6 1 1 3 3 2 | 1 3 3 2 1 ---------------+------+---------------+-------------------------------+---------------------------------------------+-----------------------------------------+---------------- x . . . . . | 2 | 960 * * | 6 3 0 0 0 0 | 3 6 12 3 0 0 0 0 0 0 | 3 6 2 6 6 1 0 0 0 0 | 1 3 3 2 0 . x . . . . | 2 | * 5760 * | 1 0 1 2 2 0 | 1 2 2 0 2 2 1 2 1 0 | 2 2 1 2 1 0 1 2 1 1 | 1 2 1 1 1 . . . . . x | 2 | * * 2880 | 0 1 0 0 4 2 | 0 0 4 2 0 2 0 2 4 1 | 0 2 0 2 4 1 0 1 2 2 | 0 1 2 2 1 ---------------+------+---------------+-------------------------------+---------------------------------------------+-----------------------------------------+---------------- x3x . . . . | 6 | 3 3 0 | 1920 * * * * * | 1 2 2 0 0 0 0 0 0 0 | 2 2 1 2 1 0 0 0 0 0 | 1 2 1 1 0 x . . . . x | 4 | 2 0 2 | * 1440 * * * * | 0 0 4 2 0 0 0 0 0 0 | 0 2 0 2 4 1 0 0 0 0 | 0 1 2 2 0 . x3o . . . | 3 | 0 3 0 | * * 1920 * * * | 1 0 0 0 2 2 0 0 0 0 | 2 2 0 0 0 0 1 2 1 0 | 1 2 1 0 1 . x . *b3o . . | 3 | 0 3 0 | * * * 3840 * * | 0 1 0 0 1 0 1 1 0 0 | 1 0 1 1 0 0 1 1 0 1 | 1 1 0 1 1 . x . . . x | 4 | 0 2 2 | * * * * 5760 * | 0 0 1 0 0 1 0 1 1 0 | 0 1 0 1 1 0 0 1 1 1 | 0 1 1 1 1 . . . . o3x | 3 | 0 0 3 | * * * * * 1920 | 0 0 0 1 0 0 0 0 2 1 | 0 0 0 0 2 1 0 0 1 2 | 0 0 1 2 1 ---------------+------+---------------+-------------------------------+---------------------------------------------+-----------------------------------------+---------------- x3x3o . . . ♦ 12 | 6 12 0 | 4 0 4 0 0 0 | 480 * * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 | 1 2 1 0 0 x3x . *b3o . . ♦ 12 | 6 12 0 | 4 0 0 4 0 0 | * 960 * * * * * * * * | 1 0 1 1 0 0 0 0 0 0 | 1 1 0 1 0 x3x . . . x ♦ 12 | 6 6 6 | 2 3 0 0 3 0 | * * 1920 * * * * * * * | 0 1 0 1 1 0 0 0 0 0 | 0 1 1 1 0 x . . . o3x ♦ 6 | 3 0 6 | 0 3 0 0 0 2 | * * * 960 * * * * * * | 0 0 0 0 2 1 0 0 0 0 | 0 0 1 2 0 . x3o *b3o . . ♦ 6 | 0 12 0 | 0 0 4 4 0 0 | * * * * 960 * * * * * | 1 0 0 0 0 0 1 1 0 0 | 1 1 0 0 1 . x3o . . x ♦ 6 | 0 6 3 | 0 0 2 0 3 0 | * * * * * 1920 * * * * | 0 1 0 0 0 0 0 1 1 0 | 0 1 1 0 1 . x . *b3o3o . ♦ 4 | 0 6 0 | 0 0 0 4 0 0 | * * * * * * 960 * * * | 0 0 1 0 0 0 1 0 0 1 | 1 0 0 1 1 . x . *b3o . x ♦ 6 | 0 6 3 | 0 0 0 2 3 0 | * * * * * * * 1920 * * | 0 0 0 1 0 0 0 1 0 1 | 0 1 0 1 1 . x . . o3x ♦ 6 | 0 3 6 | 0 0 0 0 3 2 | * * * * * * * * 1920 * | 0 0 0 0 1 0 0 0 1 1 | 0 0 1 1 1 . . . o3o3x ♦ 4 | 0 0 6 | 0 0 0 0 0 4 | * * * * * * * * * 480 | 0 0 0 0 0 1 0 0 0 2 | 0 0 0 2 1 ---------------+------+---------------+-------------------------------+---------------------------------------------+-----------------------------------------+---------------- x3x3o *b3o . . ♦ 48 | 24 96 0 | 32 0 32 32 0 0 | 8 8 0 0 8 0 0 0 0 0 | 120 * * * * * * * * * | 1 1 0 0 0 x3x3o . . x ♦ 24 | 12 24 12 | 8 6 8 0 12 0 | 2 0 4 0 0 4 0 0 0 0 | * 480 * * * * * * * * | 0 1 1 0 0 x3x . *b3o3o . ♦ 20 | 10 30 0 | 10 0 0 20 0 0 | 0 5 0 0 0 0 5 0 0 0 | * * 192 * * * * * * * | 1 0 0 1 0 x3x . *b3o . x ♦ 24 | 12 24 12 | 8 6 0 8 12 0 | 0 2 4 0 0 0 0 4 0 0 | * * * 480 * * * * * * | 0 1 0 1 0 x3x . . o3x ♦ 18 | 9 9 18 | 3 9 0 0 9 6 | 0 0 3 3 0 0 0 0 3 0 | * * * * 640 * * * * * | 0 0 1 1 0 x . . o3o3x ♦ 8 | 4 0 12 | 0 6 0 0 0 8 | 0 0 0 4 0 0 0 0 0 2 | * * * * * 240 * * * * | 0 0 0 2 0 . x3o *b3o3o . ♦ 10 | 0 30 0 | 0 0 10 20 0 0 | 0 0 0 0 5 0 5 0 0 0 | * * * * * * 192 * * * | 1 0 0 0 1 . x3o *b3o . x ♦ 12 | 0 24 6 | 0 0 8 8 12 0 | 0 0 0 0 2 4 0 4 0 0 | * * * * * * * 480 * * | 0 1 0 0 1 . x3o . o3x ♦ 9 | 0 9 9 | 0 0 3 0 9 3 | 0 0 0 0 0 3 0 0 3 0 | * * * * * * * * 640 * | 0 0 1 0 1 . x . *b3o3o3x ♦ 20 | 0 30 30 | 0 0 0 20 30 20 | 0 0 0 0 0 0 5 10 10 5 | * * * * * * * * * 192 | 0 0 0 1 1 ---------------+------+---------------+-------------------------------+---------------------------------------------+-----------------------------------------+---------------- x3x3o *b3o3o . ♦ 160 | 80 480 0 | 160 0 160 320 0 0 | 40 80 0 0 80 0 80 0 0 0 | 10 0 16 0 0 0 16 0 0 0 | 12 * * * * x3x3o *b3o . x ♦ 96 | 48 192 48 | 64 24 64 64 96 0 | 16 16 32 0 16 32 0 32 0 0 | 2 8 0 8 0 0 0 8 0 0 | * 60 * * * x3x3o . o3x ♦ 36 | 18 36 36 | 12 18 12 0 36 12 | 3 0 12 6 0 12 0 0 12 0 | 0 3 0 0 4 0 0 0 4 0 | * * 160 * * x3x . *b3o3o3x ♦ 120 | 60 180 180 | 60 90 0 120 180 120 | 0 30 60 60 0 0 30 60 60 30 | 0 0 6 15 20 15 0 0 0 6 | * * * 32 * . x3o *b3o3o3x ♦ 60 | 0 180 90 | 0 0 60 120 180 60 | 0 0 0 0 30 60 30 60 60 15 | 0 0 0 0 0 0 6 15 20 6 | * * * * 32
x3o3o3x3o4s
demi( . . . . . . ) | 1920 | 3 6 1 | 3 12 6 3 3 6 | 1 6 6 6 2 3 3 3 12 6 | 2 3 3 1 1 6 3 6 6 2 | 1 3 3 1 2
--------------------+------+---------------+-------------------------------+---------------------------------------------+-----------------------------------------+----------------
demi( x . . . . . ) | 2 | 2880 * * | 2 4 0 0 1 0 | 1 4 2 2 0 0 2 0 4 0 | 2 2 1 0 1 2 0 4 2 0 | 1 2 1 0 2
demi( . . . x . . ) | 2 | * 5760 * | 0 2 2 1 0 1 | 0 1 2 2 1 2 0 1 2 2 | 1 1 2 1 0 2 2 1 2 1 | 1 1 2 1 1
. . . . o4s | 2 | * * 960 | 0 0 0 0 3 6 | 0 0 0 0 0 0 3 3 12 6 | 0 0 0 0 1 6 3 6 6 2 | 0 3 3 1 2
--------------------+------+---------------+-------------------------------+---------------------------------------------+-----------------------------------------+----------------
demi( x3o . . . . ) | 3 | 3 0 0 | 1920 * * * * * | 1 2 0 0 0 0 1 0 0 0 | 2 1 0 0 1 0 0 2 0 0 | 1 1 0 0 2
demi( x . . x . . ) | 4 | 2 2 0 | * 5760 * * * * | 0 1 1 1 0 0 0 0 1 0 | 1 1 1 0 0 1 0 1 1 0 | 1 1 1 0 1
demi( . . o3x . . ) | 3 | 0 3 0 | * * 3840 * * * | 0 0 1 0 1 1 0 0 0 1 | 1 0 1 1 0 0 1 0 1 1 | 1 0 1 1 1
demi( . . . x3o . ) | 3 | 0 3 0 | * * * 1920 * * | 0 0 0 2 0 2 0 1 0 0 | 0 1 2 1 0 2 2 0 0 0 | 1 1 2 1 0
x . 2 . o4s | 4 | 2 0 2 | * * * * 1440 * | 0 0 0 0 0 0 2 0 4 0 | 0 0 0 0 1 2 0 4 2 0 | 0 2 1 0 2
sefa( . . . x3o4s ) | 6 | 0 3 3 | * * * * * 1920 | 0 0 0 0 0 0 0 1 2 2 | 0 0 0 0 0 2 2 1 2 1 | 0 1 2 1 1
--------------------+------+---------------+-------------------------------+---------------------------------------------+-----------------------------------------+----------------
demi( x3o3o . . . ) ♦ 4 | 6 0 0 | 4 0 0 0 0 0 | 480 * * * * * * * * * | 2 0 0 0 1 0 0 0 0 0 | 1 0 0 0 2
demi( x3o . x . . ) ♦ 6 | 6 3 0 | 2 3 0 0 0 0 | * 1920 * * * * * * * * | 1 1 0 0 0 0 0 1 0 0 | 1 1 0 0 1
demi( x . o3x . . ) ♦ 6 | 3 6 0 | 0 3 2 0 0 0 | * * 1920 * * * * * * * | 1 0 1 0 0 0 0 0 1 0 | 1 0 1 0 1
demi( x . . x3o . ) ♦ 6 | 3 6 0 | 0 3 0 2 0 0 | * * * 1920 * * * * * * | 0 1 1 0 0 1 0 0 0 0 | 1 1 1 0 0
demi( . o3o3x . . ) ♦ 4 | 0 6 0 | 0 0 4 0 0 0 | * * * * 960 * * * * * | 1 0 0 1 0 0 0 0 0 1 | 1 0 0 1 1
demi( . . o3x3o . ) ♦ 6 | 0 12 0 | 0 0 4 4 0 0 | * * * * * 960 * * * * | 0 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
x3o 2 . o4s ♦ 6 | 6 0 3 | 2 0 0 0 3 0 | * * * * * * 960 * * * | 0 0 0 0 1 0 0 2 0 0 | 0 1 0 0 2
x3o4s ♦ 12 | 0 12 6 | 0 0 0 4 0 4 | * * * * * * * 480 * * | 0 0 0 0 0 2 2 0 0 0 | 0 1 2 1 0
sefa( x . 2 x3o4s ) ♦ 12 | 6 6 6 | 0 3 0 0 3 2 | * * * * * * * * 1920 * | 0 0 0 0 0 1 0 1 1 0 | 0 1 1 0 1
sefa( . . o3x3o4s ) ♦ 12 | 0 12 6 | 0 0 4 0 0 4 | * * * * * * * * * 960 | 0 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1
--------------------+------+---------------+-------------------------------+---------------------------------------------+-----------------------------------------+----------------
demi( x3o3o3x . . ) ♦ 20 | 30 30 0 | 20 30 20 0 0 0 | 5 10 10 0 5 0 0 0 0 0 | 192 * * * * * * * * * | 1 0 0 0 1
demi( x3o . x3o . ) ♦ 9 | 9 9 0 | 3 9 0 3 0 0 | 0 3 0 3 0 0 0 0 0 0 | * 640 * * * * * * * * | 1 1 0 0 0
demi( x . o3x3o . ) ♦ 12 | 6 24 0 | 0 12 8 8 0 0 | 0 0 4 4 0 2 0 0 0 0 | * * 480 * * * * * * * | 1 0 1 0 0
demi( . o3o3x3o . ) ♦ 10 | 0 30 0 | 0 0 20 10 0 0 | 0 0 0 0 5 5 0 0 0 0 | * * * 192 * * * * * * | 1 0 0 1 0
x3o3o 2 o4s ♦ 8 | 12 0 4 | 8 0 0 0 6 0 | 2 0 0 0 0 0 4 0 0 0 | * * * * 240 * * * * * | 0 0 0 0 2
x . 2 x3o4s ♦ 24 | 12 24 12 | 0 12 0 8 6 8 | 0 0 0 4 0 0 0 2 4 0 | * * * * * 480 * * * * | 0 1 1 0 0
. . o3x3o4s ♦ 48 | 0 96 24 | 0 0 32 32 0 32 | 0 0 0 0 0 8 0 8 0 8 | * * * * * * 120 * * * | 0 0 1 1 0
sefa( x3o 2 x3o4s ) ♦ 18 | 18 9 9 | 6 9 0 0 9 3 | 0 3 0 0 0 0 3 0 3 0 | * * * * * * * 640 * * | 0 1 0 0 1
sefa( x 2 o3x3o4s ) ♦ 24 | 12 24 12 | 0 12 8 0 6 8 | 0 0 4 0 0 0 0 0 4 2 | * * * * * * * * 480 * | 0 0 1 0 1
sefa( . o3o3x3o4s ) ♦ 20 | 0 30 10 | 0 0 20 0 0 10 | 0 0 0 0 5 0 0 0 0 5 | * * * * * * * * * 192 | 0 0 0 1 1
--------------------+------+---------------+-------------------------------+---------------------------------------------+-----------------------------------------+----------------
demi( x3o3o3x3o . ) ♦ 60 | 90 180 0 | 60 180 120 60 0 0 | 15 60 60 60 30 30 0 0 0 0 | 6 20 15 6 0 0 0 0 0 0 | 32 * * * *
x3o 2 x3o4s ♦ 36 | 36 36 18 | 12 36 0 12 18 12 | 0 12 0 12 0 0 6 3 12 0 | 0 4 0 0 0 3 0 4 0 0 | * 160 * * *
x 2 o3x3o4s ♦ 96 | 48 192 48 | 0 96 64 64 24 64 | 0 0 32 32 0 16 0 16 32 16 | 0 0 8 0 0 8 2 0 8 0 | * * 60 * *
. o3o3x3o4s ♦ 160 | 0 480 80 | 0 0 320 160 0 160 | 0 0 0 0 80 80 0 40 0 80 | 0 0 0 16 0 0 10 0 0 16 | * * * 12 *
sefa( x3o3o3x3o4s ) ♦ 120 | 180 180 60 | 120 180 120 0 90 60 | 30 60 60 0 30 0 60 0 60 30 | 6 0 0 0 15 0 0 20 15 6 | * * * * 32
starting figure: x3o3o3x3o4x
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