stericated penteract,
stericated pentacross
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| Acronym | scant |
| Name |
small cellated penteractitriacontiditeron, stericated penteract, stericated pentacross |
| Circumradius | sqrt[7+2 sqrt(2)]/2 = 1.567516 |
| Vertex figure |
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| Coordinates | ((1+sqrt(2))/2, 1/2, 1/2, 1/2, 1/2) & all permutations, all changes of sign |
| General of army | (is itself convex) |
| Colonel of regiment | (is itself locally convex – other uniform polyteral members: sinnont & others) |
| Confer | |
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External links |
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Incidence matrix according to Dynkin symbol
x3o3o3o4x . . . . . | 160 | 4 4 | 6 12 6 | 4 12 12 4 | 1 4 6 4 1 ----------+-----+---------+-------------+----------------+--------------- x . . . . | 2 | 320 * | 3 3 0 | 3 6 3 0 | 1 3 3 1 0 . . . . x | 2 | * 320 | 0 3 3 | 0 3 6 3 | 0 1 3 3 1 ----------+-----+---------+-------------+----------------+--------------- x3o . . . | 3 | 3 0 | 320 * * | 2 2 0 0 | 1 2 1 0 0 x . . . x | 4 | 2 2 | * 480 * | 0 2 2 0 | 0 1 2 1 0 . . . o4x | 4 | 0 4 | * * 240 | 0 0 2 2 | 0 0 1 2 1 ----------+-----+---------+-------------+----------------+--------------- x3o3o . . ♦ 4 | 6 0 | 4 0 0 | 160 * * * | 1 1 0 0 0 x3o . . x ♦ 6 | 6 3 | 2 3 0 | * 320 * * | 0 1 1 0 0 x . . o4x ♦ 8 | 4 8 | 0 4 2 | * * 240 * | 0 0 1 1 0 . . o3o4x ♦ 8 | 0 12 | 0 0 6 | * * * 80 | 0 0 0 1 1 ----------+-----+---------+-------------+----------------+--------------- x3o3o3o . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 0 | 32 * * * * x3o3o . x ♦ 8 | 12 4 | 8 6 0 | 2 4 0 0 | * 80 * * * x3o . o4x ♦ 12 | 12 12 | 4 12 3 | 0 4 3 0 | * * 80 * * x . o3o4x ♦ 16 | 8 24 | 0 12 12 | 0 0 6 2 | * * * 40 * . o3o3o4x ♦ 16 | 0 32 | 0 0 24 | 0 0 0 8 | * * * * 10
oxxo3oooo3oooo4xxxx&#xt → outer heights = 1/sqrt(2) = 0.707107
central height = 1
(tes || pseudo sidpith || pseudo sidpith || tes)
o...3o...3o...4o... & | 32 * | 4 4 0 0 0 | 6 6 12 0 0 0 0 0 | 4 4 12 12 0 0 0 0 0 0 0 | 1 1 4 6 4 0 0 0 0
.o..3.o..3.o..4.o.. & | * 128 | 0 1 3 3 1 | 0 3 3 3 6 3 3 3 | 0 3 6 3 1 3 3 1 3 6 3 | 0 1 3 3 1 1 3 3 1
--------------------------+--------+-------------------+-----------------------------+------------------------------------+-------------------------
.... .... .... x... & | 2 0 | 64 * * * * | 3 0 3 0 0 0 0 0 | 3 0 3 6 0 0 0 0 0 0 0 | 1 0 1 3 3 0 0 0 0
oo..3oo..3oo..4oo..&#x & | 1 1 | * 128 * * * | 0 3 3 0 0 0 0 0 | 0 3 6 3 0 0 0 0 0 0 0 | 0 1 3 3 1 0 0 0 0
.x.. .... .... .... & | 0 2 | * * 192 * * | 0 1 0 2 2 0 1 0 | 0 2 2 0 1 2 1 0 2 2 0 | 0 1 2 1 0 1 2 1 0
.... .... .... .x.. & | 0 2 | * * * 192 * | 0 0 1 0 2 2 0 1 | 0 0 2 2 0 1 2 1 0 2 0 | 0 0 1 2 1 0 1 2 1
.oo.3.oo.3.oo.4.oo.&#x | 0 2 | * * * * 64 | 0 0 0 0 0 0 3 3 | 0 0 0 0 0 0 0 0 3 6 3 | 0 0 0 0 0 1 3 3 1
--------------------------+--------+-------------------+-----------------------------+------------------------------------+-------------------------
.... .... o...4x... & | 4 0 | 4 0 0 0 0 | 48 * * * * * * * | 2 0 0 2 0 0 0 0 0 0 0 | 1 0 0 1 2 0 0 0 0
ox.. .... .... ....&#x & | 1 2 | 0 2 1 0 0 | * 192 * * * * * * | 0 2 2 0 0 0 0 0 0 0 0 | 0 1 2 1 0 0 0 0 0
.... .... .... xx..&#x & | 2 2 | 1 2 0 1 0 | * * 192 * * * * * | 0 0 2 2 0 0 0 0 0 0 0 | 0 0 1 2 1 0 0 0 0
.x..3.o.. .... .... & | 0 3 | 0 0 3 0 0 | * * * 128 * * * * | 0 1 0 0 1 1 0 0 1 0 0 | 0 1 1 0 0 1 1 0 0
.x.. .... .... .x.. & | 0 4 | 0 0 2 2 0 | * * * * 192 * * * | 0 0 1 0 0 1 1 0 0 1 0 | 0 0 1 1 0 0 1 1 0
.... .... .o..4.x.. & | 0 4 | 0 0 0 4 0 | * * * * * 96 * * | 0 0 0 1 0 0 1 1 0 0 1 | 0 0 0 1 1 0 0 1 1
.xx. .... .... .... | 0 4 | 0 0 2 0 2 | * * * * * * 96 * | 0 0 0 0 0 0 0 0 2 2 0 | 0 0 0 0 0 1 2 1 0
.... .... .... .xx. | 0 4 | 0 0 0 2 2 | * * * * * * * 96 | 0 0 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 0 1 2 1
--------------------------+--------+-------------------+-----------------------------+------------------------------------+-------------------------
.... o...3o...4x... & ♦ 8 0 | 12 0 0 0 0 | 6 0 0 0 0 0 0 0 | 16 * * * * * * * * * * | 1 0 0 0 1 0 0 0 0
ox..3oo.. .... ....&#x & ♦ 1 3 | 0 3 3 0 0 | 0 3 0 1 0 0 0 0 | * 128 * * * * * * * * * | 0 1 1 0 0 0 0 0 0
ox.. .... .... xx..&#x & ♦ 2 4 | 1 4 2 2 0 | 0 2 2 0 1 0 0 0 | * * 192 * * * * * * * * | 0 0 1 1 0 0 0 0 0
.... .... oo..4xx..&#x & ♦ 4 4 | 4 4 0 4 0 | 1 0 4 0 0 1 0 0 | * * * 96 * * * * * * * | 0 0 0 1 1 0 0 0 0
.x..3.o..3.o.. .... & ♦ 0 4 | 0 0 6 0 0 | 0 0 0 4 0 0 0 0 | * * * * 32 * * * * * * | 0 1 0 0 0 1 0 0 0
.x..3.o.. .... .x.. & ♦ 0 6 | 0 0 6 3 0 | 0 0 0 2 3 0 0 0 | * * * * * 64 * * * * * | 0 0 1 0 0 0 1 0 0
.x.. .... .o..4.x.. & ♦ 0 8 | 0 0 4 8 0 | 0 0 0 0 4 2 0 0 | * * * * * * 48 * * * * | 0 0 0 1 0 0 0 1 0
.... .o..3.o..4.x.. & ♦ 0 8 | 0 0 0 12 0 | 0 0 0 0 0 6 0 0 | * * * * * * * 16 * * * | 0 0 0 0 1 0 0 0 1
.xx.3.oo. .... ....&#x ♦ 0 6 | 0 0 6 0 3 | 0 0 0 2 0 0 3 0 | * * * * * * * * 64 * * | 0 0 0 0 0 1 1 0 0
.xx. .... .... .xx.&#x ♦ 0 8 | 0 0 4 4 4 | 0 0 0 0 2 0 2 2 | * * * * * * * * * 96 * | 0 0 0 0 0 0 1 1 0
.... .... .oo.4.xx.&#x ♦ 0 8 | 0 0 0 8 4 | 0 0 0 0 0 2 0 4 | * * * * * * * * * * 48 | 0 0 0 0 0 0 0 1 1
--------------------------+--------+-------------------+-----------------------------+------------------------------------+-------------------------
o...3o...3o...4x... & ♦ 16 0 | 32 0 0 0 0 | 24 0 0 0 0 0 0 0 | 8 0 0 0 0 0 0 0 0 0 0 | 2 * * * * * * * *
ox..3oo..3oo.. ....&#x & ♦ 1 4 | 0 4 6 0 0 | 0 6 0 4 0 0 0 0 | 0 4 0 0 1 0 0 0 0 0 0 | * 32 * * * * * * *
ox..3oo.. .... xx..&#x & ♦ 2 6 | 1 6 6 3 0 | 0 6 3 2 3 0 0 0 | 0 2 3 0 0 1 0 0 0 0 0 | * * 64 * * * * * *
ox.. .... oo..4xx..&#x & ♦ 4 8 | 4 8 4 8 0 | 1 4 8 0 4 2 0 0 | 0 0 4 2 0 0 1 0 0 0 0 | * * * 48 * * * * *
.... oo..3oo..4xx..&#x & ♦ 8 8 | 12 8 0 12 0 | 6 0 12 0 0 6 0 0 | 1 0 0 6 0 0 0 1 0 0 0 | * * * * 16 * * * *
.xx.3.oo.3.oo. ....&#x ♦ 0 8 | 0 0 12 0 4 | 0 0 0 8 0 0 6 0 | 0 0 0 0 2 0 0 0 4 0 0 | * * * * * 16 * * *
.xx.3.oo. .... .xx.&#x ♦ 0 12 | 0 0 12 6 6 | 0 0 0 4 6 0 6 3 | 0 0 0 0 0 2 0 0 2 3 0 | * * * * * * 32 * *
.xx. .... .oo.4.xx.&#x ♦ 0 16 | 0 0 8 16 8 | 0 0 0 0 8 4 4 8 | 0 0 0 0 0 0 2 0 0 4 2 | * * * * * * * 24 *
.... .oo.3.oo.4.xx.&#x ♦ 0 16 | 0 0 0 24 8 | 0 0 0 0 0 12 0 12 | 0 0 0 0 0 0 0 2 0 0 6 | * * * * * * * * 8
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