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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), 1+2 sqrt(2), 1+sqrt(2), 1+sqrt(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
o3x3/2o3/2x4x
. . . . . | 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
. x3/2o . . | 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
. . o3/2x . | 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
--------------+-----+--------------+-------------------------+----------------------------+------------
o3x3/2o . . ♦ 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
. x3/2o3/2x . ♦ 12 | 12 12 0 | 0 4 6 0 4 0 | * * * 160 * * * | 1 0 0 1
. x3/2o . 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
. . o3/2x4x ♦ 24 | 0 24 12 | 0 0 0 0 8 6 | * * * * * * 40 | 0 0 0 2
--------------+-----+--------------+-------------------------+----------------------------+------------
o3x3/2o3/2x . ♦ 30 | 60 30 0 | 20 20 30 0 10 0 | 5 10 0 5 0 0 0 | 32 * * *
o3x3/2o . 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 *
. x3/2o3/2x4x ♦ 192 | 192 192 96 | 0 64 96 96 64 48 | 0 0 0 16 32 24 8 | * * * 10
o3/2x3o3x4x
. . . . . | 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
------------+-----+--------------+-------------------------+----------------------------+------------
o3/2x . . . | 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
------------+-----+--------------+-------------------------+----------------------------+------------
o3/2x3o . . ♦ 6 | 12 0 0 | 4 4 0 0 0 0 | 160 * * * * * * | 1 1 0 0
o3/2x . x . ♦ 6 | 6 3 0 | 2 0 3 0 0 0 | * 320 * * * * * | 1 0 1 0
o3/2x . . 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
------------+-----+--------------+-------------------------+----------------------------+------------
o3/2x3o3x . ♦ 30 | 60 30 0 | 20 20 30 0 10 0 | 5 10 0 5 0 0 0 | 32 * * *
o3/2x3o . x ♦ 12 | 24 0 6 | 8 8 0 12 0 0 | 2 0 4 0 4 0 0 | * 80 * *
o3/2x . 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
o3/2x3/2o3/2x4x
. . . . . | 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
----------------+-----+--------------+-------------------------+----------------------------+------------
o3/2x . . . | 3 | 3 0 0 | 640 * * * * * | 1 1 1 0 0 0 0 | 1 1 1 0
. x3/2o . . | 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
. . o3/2x . | 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
----------------+-----+--------------+-------------------------+----------------------------+------------
o3/2x3/2o . . ♦ 6 | 12 0 0 | 4 4 0 0 0 0 | 160 * * * * * * | 1 1 0 0
o3/2x . x . ♦ 6 | 6 3 0 | 2 0 3 0 0 0 | * 320 * * * * * | 1 0 1 0
o3/2x . . x ♦ 6 | 6 0 3 | 2 0 0 3 0 0 | * * 320 * * * * | 0 1 1 0
. x3/2o3/2x . ♦ 12 | 12 12 0 | 0 4 6 0 4 0 | * * * 160 * * * | 1 0 0 1
. x3/2o . 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
. . o3/2x4x ♦ 24 | 0 24 12 | 0 0 0 0 8 6 | * * * * * * 40 | 0 0 0 2
----------------+-----+--------------+-------------------------+----------------------------+------------
o3/2x3/2o3/2x . ♦ 30 | 60 30 0 | 20 20 30 0 10 0 | 5 10 0 5 0 0 0 | 32 * * *
o3/2x3/2o . x ♦ 12 | 24 0 6 | 8 8 0 12 0 0 | 2 0 4 0 4 0 0 | * 80 * *
o3/2x . x4x ♦ 24 | 24 12 12 | 8 0 12 12 0 3 | 0 4 4 0 0 3 0 | * * 80 *
. x3/2o3/2x4x ♦ 192 | 192 192 96 | 0 64 96 96 64 48 | 0 0 0 16 32 24 8 | * * * 10
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)
...