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Acronym
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prin
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Name
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prismatorhombated penteract,
runcicantellated penteract
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Field of sections
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 ©
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Circumradius
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sqrt[23+10 sqrt(2)]/2 = 3.047217
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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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x3o4x u3o4x x3x4x x3x4x u3o4x x3o4x -- x3x3o4x (prit)
u3o4x o3u4x o3u4x u3o4x -- o3u3o4x ((u,x)-srit)
x3x4x o3u4x o3x4w o3x4w o3u4x x3x4x -- o3x3x4x (grit)
x3x4x o3u4x o3x4w o3x4w o3u4x x3x4x -- o3x3x4x (grit)
u3o4x o3u4x o3u4x u3o4x -- o3u3o4x ((u,x)-srit)
x3o4x u3o4x x3x4x x3x4x u3o4x x3o4x -- x3x3o4x (prit)
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Coordinates
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(1+2 sqrt(2), 1+2 sqrt(2), 1+sqrt(2), 1, 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, 2880, 2960, 1240, 202
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Confer
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- related segmentotera:
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grittip
- general polytopal classes:
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Wythoffian polytera
partial Stott expansions
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External
links
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As abstract polyteron prin is isomorph to quiprin, thereby replacing prograde by retrograde squares,
resp. sirco by querco,
resp. prit by paqrit.
Incidence matrix according to Dynkin symbol
o3x3x3o4x
. . . . . | 960 | 2 2 2 | 1 4 4 1 2 1 | 2 2 2 4 2 1 | 1 2 1 2
----------+-----+-------------+-------------------------+------------------------+------------
. x . . . | 2 | 960 * * | 1 2 2 0 0 0 | 2 2 1 2 1 0 | 1 2 1 1
. . x . . | 2 | * 960 * | 0 2 0 1 1 0 | 1 0 2 2 0 1 | 1 1 0 2
. . . . x | 2 | * * 960 | 0 0 2 0 1 1 | 0 1 0 2 2 1 | 0 1 1 2
----------+-----+-------------+-------------------------+------------------------+------------
o3x . . . | 3 | 3 0 0 | 320 * * * * * | 2 2 0 0 0 0 | 1 2 1 0
. x3x . . | 6 | 3 3 0 | * 640 * * * * | 1 0 1 1 0 0 | 1 1 0 1
. x . . x | 4 | 2 0 2 | * * 960 * * * | 0 1 0 1 1 0 | 0 1 1 1
. . x3o . | 3 | 0 3 0 | * * * 320 * * | 0 0 2 0 0 1 | 1 0 0 2
. . x . x | 4 | 0 2 2 | * * * * 480 * | 0 0 0 2 0 1 | 0 1 0 2
. . . o4x | 4 | 0 0 4 | * * * * * 240 | 0 0 0 0 2 1 | 0 0 1 2
----------+-----+-------------+-------------------------+------------------------+------------
o3x3x . . ♦ 12 | 12 6 0 | 4 4 0 0 0 0 | 160 * * * * * | 1 1 0 0
o3x . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 | * 320 * * * * | 0 1 1 0
. x3x3o . ♦ 12 | 6 12 0 | 0 4 0 4 0 0 | * * 160 * * * | 1 0 0 1
. x3x . x ♦ 12 | 6 6 6 | 0 2 3 0 3 0 | * * * 320 * * | 0 1 0 1
. x . o4x ♦ 8 | 4 0 8 | 0 0 4 0 0 2 | * * * * 240 * | 0 0 1 1
. . x3o4x ♦ 24 | 0 24 24 | 0 0 0 8 12 6 | * * * * * 40 | 0 0 0 2
----------+-----+-------------+-------------------------+------------------------+------------
o3x3x3o . ♦ 30 | 30 30 0 | 10 20 0 10 0 0 | 5 0 5 0 0 0 | 32 * * *
o3x3x . x ♦ 24 | 24 12 12 | 8 8 12 0 6 0 | 2 4 0 4 0 0 | * 80 * *
o3x . o4x ♦ 12 | 12 0 12 | 4 0 12 0 0 3 | 0 4 0 0 3 0 | * * 80 *
. x3x3o4x ♦ 192 | 96 192 192 | 0 64 96 64 96 48 | 0 0 16 32 24 8 | * * * 10
snubbed forms: o3x3x3o4s
o3x3x3/2o4/3x
. . . . . | 960 | 2 2 2 | 1 4 4 1 2 1 | 2 2 2 4 2 1 | 1 2 1 2
--------------+-----+-------------+-------------------------+------------------------+------------
. x . . . | 2 | 960 * * | 1 2 2 0 0 0 | 2 2 1 2 1 0 | 1 2 1 1
. . x . . | 2 | * 960 * | 0 2 0 1 1 0 | 1 0 2 2 0 1 | 1 1 0 2
. . . . x | 2 | * * 960 | 0 0 2 0 1 1 | 0 1 0 2 2 1 | 0 1 1 2
--------------+-----+-------------+-------------------------+------------------------+------------
o3x . . . | 3 | 3 0 0 | 320 * * * * * | 2 2 0 0 0 0 | 1 2 1 0
. x3x . . | 6 | 3 3 0 | * 640 * * * * | 1 0 1 1 0 0 | 1 1 0 1
. x . . x | 4 | 2 0 2 | * * 960 * * * | 0 1 0 1 1 0 | 0 1 1 1
. . x3/2o . | 3 | 0 3 0 | * * * 320 * * | 0 0 2 0 0 1 | 1 0 0 2
. . x . x | 4 | 0 2 2 | * * * * 480 * | 0 0 0 2 0 1 | 0 1 0 2
. . . o4/3x | 4 | 0 0 4 | * * * * * 240 | 0 0 0 0 2 1 | 0 0 1 2
--------------+-----+-------------+-------------------------+------------------------+------------
o3x3x . . ♦ 12 | 12 6 0 | 4 4 0 0 0 0 | 160 * * * * * | 1 1 0 0
o3x . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 | * 320 * * * * | 0 1 1 0
. x3x3/2o . ♦ 12 | 6 12 0 | 0 4 0 4 0 0 | * * 160 * * * | 1 0 0 1
. x3x . x ♦ 12 | 6 6 6 | 0 2 3 0 3 0 | * * * 320 * * | 0 1 0 1
. x . o4/3x ♦ 8 | 4 0 8 | 0 0 4 0 0 2 | * * * * 240 * | 0 0 1 1
. . x3/2o4/3x ♦ 24 | 0 24 24 | 0 0 0 8 12 6 | * * * * * 40 | 0 0 0 2
--------------+-----+-------------+-------------------------+------------------------+------------
o3x3x3/2o . ♦ 30 | 30 30 0 | 10 20 0 10 0 0 | 5 0 5 0 0 0 | 32 * * *
o3x3x . x ♦ 24 | 24 12 12 | 8 8 12 0 6 0 | 2 4 0 4 0 0 | * 80 * *
o3x . o4/3x ♦ 12 | 12 0 12 | 4 0 12 0 0 3 | 0 4 0 0 3 0 | * * 80 *
. x3x3/2o4/3x ♦ 192 | 96 192 192 | 0 64 96 64 96 48 | 0 0 16 32 24 8 | * * * 10
o3/2x3x3o4x
. . . . . | 960 | 2 2 2 | 1 4 4 1 2 1 | 2 2 2 4 2 1 | 1 2 1 2
------------+-----+-------------+-------------------------+------------------------+------------
. x . . . | 2 | 960 * * | 1 2 2 0 0 0 | 2 2 1 2 1 0 | 1 2 1 1
. . x . . | 2 | * 960 * | 0 2 0 1 1 0 | 1 0 2 2 0 1 | 1 1 0 2
. . . . x | 2 | * * 960 | 0 0 2 0 1 1 | 0 1 0 2 2 1 | 0 1 1 2
------------+-----+-------------+-------------------------+------------------------+------------
o3/2x . . . | 3 | 3 0 0 | 320 * * * * * | 2 2 0 0 0 0 | 1 2 1 0
. x3x . . | 6 | 3 3 0 | * 640 * * * * | 1 0 1 1 0 0 | 1 1 0 1
. x . . x | 4 | 2 0 2 | * * 960 * * * | 0 1 0 1 1 0 | 0 1 1 1
. . x3o . | 3 | 0 3 0 | * * * 320 * * | 0 0 2 0 0 1 | 1 0 0 2
. . x . x | 4 | 0 2 2 | * * * * 480 * | 0 0 0 2 0 1 | 0 1 0 2
. . . o4x | 4 | 0 0 4 | * * * * * 240 | 0 0 0 0 2 1 | 0 0 1 2
------------+-----+-------------+-------------------------+------------------------+------------
o3/2x3x . . ♦ 12 | 12 6 0 | 4 4 0 0 0 0 | 160 * * * * * | 1 1 0 0
o3/2x . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 | * 320 * * * * | 0 1 1 0
. x3x3o . ♦ 12 | 6 12 0 | 0 4 0 4 0 0 | * * 160 * * * | 1 0 0 1
. x3x . x ♦ 12 | 6 6 6 | 0 2 3 0 3 0 | * * * 320 * * | 0 1 0 1
. x . o4x ♦ 8 | 4 0 8 | 0 0 4 0 0 2 | * * * * 240 * | 0 0 1 1
. . x3o4x ♦ 24 | 0 24 24 | 0 0 0 8 12 6 | * * * * * 40 | 0 0 0 2
------------+-----+-------------+-------------------------+------------------------+------------
o3/2x3x3o . ♦ 30 | 30 30 0 | 10 20 0 10 0 0 | 5 0 5 0 0 0 | 32 * * *
o3/2x3x . x ♦ 24 | 24 12 12 | 8 8 12 0 6 0 | 2 4 0 4 0 0 | * 80 * *
o3/2x . o4x ♦ 12 | 12 0 12 | 4 0 12 0 0 3 | 0 4 0 0 3 0 | * * 80 *
. x3x3o4x ♦ 192 | 96 192 192 | 0 64 96 64 96 48 | 0 0 16 32 24 8 | * * * 10
o3/2x3x3/2o4/3x
. . . . . | 960 | 2 2 2 | 1 4 4 1 2 1 | 2 2 2 4 2 1 | 1 2 1 2
----------------+-----+-------------+-------------------------+------------------------+------------
. x . . . | 2 | 960 * * | 1 2 2 0 0 0 | 2 2 1 2 1 0 | 1 2 1 1
. . x . . | 2 | * 960 * | 0 2 0 1 1 0 | 1 0 2 2 0 1 | 1 1 0 2
. . . . x | 2 | * * 960 | 0 0 2 0 1 1 | 0 1 0 2 2 1 | 0 1 1 2
----------------+-----+-------------+-------------------------+------------------------+------------
o3/2x . . . | 3 | 3 0 0 | 320 * * * * * | 2 2 0 0 0 0 | 1 2 1 0
. x3x . . | 6 | 3 3 0 | * 640 * * * * | 1 0 1 1 0 0 | 1 1 0 1
. x . . x | 4 | 2 0 2 | * * 960 * * * | 0 1 0 1 1 0 | 0 1 1 1
. . x3/2o . | 3 | 0 3 0 | * * * 320 * * | 0 0 2 0 0 1 | 1 0 0 2
. . x . x | 4 | 0 2 2 | * * * * 480 * | 0 0 0 2 0 1 | 0 1 0 2
. . . o4/3x | 4 | 0 0 4 | * * * * * 240 | 0 0 0 0 2 1 | 0 0 1 2
----------------+-----+-------------+-------------------------+------------------------+------------
o3/2x3x . . ♦ 12 | 12 6 0 | 4 4 0 0 0 0 | 160 * * * * * | 1 1 0 0
o3/2x . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 0 | * 320 * * * * | 0 1 1 0
. x3x3/2o . ♦ 12 | 6 12 0 | 0 4 0 4 0 0 | * * 160 * * * | 1 0 0 1
. x3x . x ♦ 12 | 6 6 6 | 0 2 3 0 3 0 | * * * 320 * * | 0 1 0 1
. x . o4/3x ♦ 8 | 4 0 8 | 0 0 4 0 0 2 | * * * * 240 * | 0 0 1 1
. . x3/2o4/3x ♦ 24 | 0 24 24 | 0 0 0 8 12 6 | * * * * * 40 | 0 0 0 2
----------------+-----+-------------+-------------------------+------------------------+------------
o3/2x3x3/2o . ♦ 30 | 30 30 0 | 10 20 0 10 0 0 | 5 0 5 0 0 0 | 32 * * *
o3/2x3x . x ♦ 24 | 24 12 12 | 8 8 12 0 6 0 | 2 4 0 4 0 0 | * 80 * *
o3/2x . o4/3x ♦ 12 | 12 0 12 | 4 0 12 0 0 3 | 0 4 0 0 3 0 | * * 80 *
. x3x3/2o4/3x ♦ 192 | 96 192 192 | 0 64 96 64 96 48 | 0 0 16 32 24 8 | * * * 10