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Acronym
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pattin
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Name
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prismatotruncated penteract,
runcitruncated penteract
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Circumradius
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sqrt[25+12 sqrt(2)]/2 = 3.239235
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Vertex figure
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 ©
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Lace city
in approx. ASCII-art
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 ©
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o3x4x x3x4x x3o4w x3o4w x3x4x o3x4x -- x3o3x4x (proh)
x3x4x o3u4x o3x4w o3x4w o3u4x x3x4x -- o3x3x4x (grit)
x3o4w o3x4w o3x4w x3o4w -- o3x3o4w ((x,w)-srit)
x3o4w o3x4w o3x4w x3o4w -- o3x3o4w ((x,w)-srit)
x3x4x o3u4x o3x4w o3x4w o3u4x x3x4x -- o3x3x4x (grit)
o3x4x x3x4x x3o4w x3o4w x3x4x o3x4x -- x3o3x4x (proh)
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Coordinates
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((1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2) & all permutations, all changes of sign
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General of army
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(is itself convex)
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Colonel of regiment
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(is itself locally convex
– uniform polyteral members:
& others)
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Face vector
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960, 3360, 3760, 1560, 202
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Confer
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- general polytopal classes:
-
Wythoffian polytera
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External
links
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As abstract polyteron pattin is isomorph to quiptin, thereby replacing octagons by octagrams,
resp. op by stop and tic by quith,
resp. todip by tistodip and proh by quiproh.
Incidence matrix according to Dynkin symbol
o3x3o3x4x
. . . . . | 960 | 4 2 1 | 2 2 4 4 1 2 | 1 2 2 2 2 4 1 | 1 1 2 2
----------+-----+--------------+-------------------------+----------------------------+------------
. x . . . | 2 | 1920 * * | 1 1 1 1 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1
. . . x . | 2 | * 960 * | 0 0 2 0 1 1 | 0 1 0 2 0 2 1 | 1 0 1 2
. . . . x | 2 | * * 480 | 0 0 0 4 0 2 | 0 0 2 0 2 4 1 | 0 1 2 2
----------+-----+--------------+-------------------------+----------------------------+------------
o3x . . . | 3 | 3 0 0 | 640 * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
. x3o . . | 3 | 3 0 0 | * 640 * * * * | 1 0 0 1 1 0 0 | 1 1 0 1
. x . x . | 4 | 2 2 0 | * * 960 * * * | 0 1 0 1 0 1 0 | 1 0 1 1
. x . . x | 4 | 2 0 2 | * * * 960 * * | 0 0 1 0 1 1 0 | 0 1 1 1
. . o3x . | 3 | 0 3 0 | * * * * 320 * | 0 0 0 2 0 0 1 | 1 0 0 2
. . . x4x | 8 | 0 4 4 | * * * * * 240 | 0 0 0 0 0 2 1 | 0 0 1 2
----------+-----+--------------+-------------------------+----------------------------+------------
o3x3o . . ♦ 6 | 12 0 0 | 4 4 0 0 0 0 | 160 * * * * * * | 1 1 0 0
o3x . x . ♦ 6 | 6 3 0 | 2 0 3 0 0 0 | * 320 * * * * * | 1 0 1 0
o3x . . x ♦ 6 | 6 0 3 | 2 0 0 3 0 0 | * * 320 * * * * | 0 1 1 0
. x3o3x . ♦ 12 | 12 12 0 | 0 4 6 0 4 0 | * * * 160 * * * | 1 0 0 1
. x3o . x ♦ 6 | 6 0 3 | 0 2 0 3 0 0 | * * * * 320 * * | 0 1 0 1
. x . x4x ♦ 16 | 8 8 8 | 0 0 4 4 2 2 | * * * * * 240 * | 0 0 1 1
. . o3x4x ♦ 24 | 0 24 12 | 0 0 0 0 8 6 | * * * * * * 40 | 0 0 0 2
----------+-----+--------------+-------------------------+----------------------------+------------
o3x3o3x . ♦ 30 | 60 30 0 | 20 20 30 0 10 0 | 5 10 0 5 0 0 0 | 32 * * *
o3x3o . x ♦ 12 | 24 0 6 | 8 8 0 12 0 0 | 2 0 4 0 4 0 0 | * 80 * *
o3x . x4x ♦ 24 | 24 12 12 | 8 0 12 12 0 3 | 0 4 4 0 0 3 0 | * * 80 *
. x3o3x4x ♦ 192 | 192 192 96 | 0 64 96 96 64 48 | 0 0 0 16 32 24 8 | * * * 10
snubbed forms: o3x3o3x4s
xoooox3oxxxxo3xxooxx4xxwwxx&#xt → height(1,2) = height(2,3) = height(4,5) = height(5,6) = 1/sqrt(2) = 0.707107
height(3,4) = 1
(proh || pseudo grit || pseudo (x,w)-srit || (x,w)-srit || pseudo grit || proh)
...