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Acronym
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captid (old: hiptid)
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Name
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celliprismatotruncated dodecateron,
hedratoprismatotruncated dodecateron,
steriruncitruncated hexateron
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Field of sections
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 ©
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Circumradius
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sqrt(5) = 2.236068
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Vertex figure
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 ©  ©
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Lace city
in approx. ASCII-art
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x3x3o x3x3o
x3x3x x3x3x
u3o3x x3x3u x3x3u u3o3x
x3o3x u3o3u x3u3x u3o3u x3o3x
x3o3u u3x3x u3x3x x3o3u
x3x3x x3x3x
o3x3x o3x3x
\_ \_ \_ \_ \_
\_ \_ \_ \_ +-- x3x3o3x (prip)
\_ \_ \_ +--------- x3x3o3u ((x,x,u)-prip)
\_ \_ +---------------- x3x3x3x (gippid)
\_ +----------------------- u3o3x3x (inv. (x,x,u)-prip)
+------------------------------ x3o3x3x (inv. prip)
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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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Confer
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pripro
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Face vector
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360, 1080, 1110, 450, 62
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Confer
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- general polytopal classes:
-
Wythoffian polytera
lace simplices
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External
links
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Incidence matrix according to Dynkin symbol
x3x3o3x3x
. . . . . | 360 | 1 2 2 1 | 2 2 1 1 2 2 1 2 | 1 2 2 1 2 1 1 2 1 | 1 1 2 1 1
----------+-----+-----------------+--------------------------------+----------------------------+-------------
x . . . . | 2 | 180 * * * | 2 2 1 0 0 0 0 0 | 1 2 2 1 2 0 0 0 0 | 1 1 2 1 0
. x . . . | 2 | * 360 * * | 1 0 0 1 1 1 0 0 | 1 1 1 0 0 1 1 1 0 | 1 1 1 0 1
. . . x . | 2 | * * 360 * | 0 1 0 0 1 0 1 1 | 0 1 0 1 1 1 0 1 1 | 1 0 1 1 1
. . . . x | 2 | * * * 180 | 0 0 1 0 0 2 0 2 | 0 0 2 0 2 0 1 2 1 | 0 1 2 1 1
----------+-----+-----------------+--------------------------------+----------------------------+-------------
x3x . . . | 6 | 3 3 0 0 | 120 * * * * * * * | 1 1 1 0 0 0 0 0 0 | 1 1 1 0 0
x . . x . | 4 | 2 0 2 0 | * 180 * * * * * * | 0 1 0 1 1 0 0 0 0 | 1 0 1 1 0
x . . . x | 4 | 2 0 0 2 | * * 90 * * * * * | 0 0 2 0 2 0 0 0 0 | 0 1 2 1 0
. x3o . . | 3 | 0 3 0 0 | * * * 120 * * * * | 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1
. x . x . | 4 | 0 2 2 0 | * * * * 180 * * * | 0 1 0 0 0 1 0 1 0 | 1 0 1 0 1
. x . . x | 4 | 0 2 0 2 | * * * * * 180 * * | 0 0 1 0 0 0 1 1 0 | 0 1 1 0 1
. . o3x . | 3 | 0 0 3 0 | * * * * * * 120 * | 0 0 0 1 0 1 0 0 1 | 1 0 0 1 1
. . . x3x | 6 | 0 0 3 3 | * * * * * * * 120 | 0 0 0 0 1 0 0 1 1 | 0 0 1 1 1
----------+-----+-----------------+--------------------------------+----------------------------+-------------
x3x3o . . ♦ 12 | 6 12 0 0 | 4 0 0 4 0 0 0 0 | 30 * * * * * * * * | 1 1 0 0 0
x3x . x . ♦ 12 | 6 6 6 0 | 2 3 0 0 3 0 0 0 | * 60 * * * * * * * | 1 0 1 0 0
x3x . . x ♦ 12 | 6 6 0 6 | 2 0 3 0 0 3 0 0 | * * 60 * * * * * * | 0 1 1 0 0
x . o3x . ♦ 6 | 3 0 6 0 | 0 3 0 0 0 0 2 0 | * * * 60 * * * * * | 1 0 0 1 0
x . . x3x ♦ 12 | 6 0 6 6 | 0 3 3 0 0 0 0 2 | * * * * 60 * * * * | 0 0 1 1 0
. x3o3x . ♦ 12 | 0 12 12 0 | 0 0 0 4 6 0 4 0 | * * * * * 30 * * * | 1 0 0 0 1
. x3o . x ♦ 6 | 0 6 0 3 | 0 0 0 2 0 3 0 0 | * * * * * * 60 * * | 0 1 0 0 1
. x . x3x ♦ 12 | 0 6 6 6 | 0 0 0 0 3 3 0 2 | * * * * * * * 60 * | 0 0 1 0 1
. . o3x3x ♦ 12 | 0 0 12 6 | 0 0 0 0 0 0 4 4 | * * * * * * * * 30 | 0 0 0 1 1
----------+-----+-----------------+--------------------------------+----------------------------+-------------
x3x3o3x . ♦ 60 | 30 60 60 0 | 20 30 0 20 30 0 20 0 | 5 10 0 10 0 5 0 0 0 | 6 * * * *
x3x3o . x ♦ 24 | 12 24 0 12 | 8 0 6 8 0 12 0 0 | 2 0 4 0 0 0 4 0 0 | * 15 * * *
x3x . x3x ♦ 36 | 18 18 18 18 | 6 9 9 0 9 9 0 6 | 0 3 3 0 3 0 0 3 0 | * * 20 * *
x . o3x3x ♦ 24 | 12 0 24 12 | 0 12 6 0 0 0 8 8 | 0 0 0 4 4 0 0 0 2 | * * * 15 *
. x3o3x3x ♦ 60 | 0 60 60 30 | 0 0 0 20 30 30 20 20 | 0 0 0 0 0 5 10 10 5 | * * * * 6
or
. . . . . | 360 | 2 4 | 4 4 1 2 2 | 2 4 4 2 1 | 2 2 2
-------------+-----+---------+--------------------+-------------------+---------
x . . . . & | 2 | 360 * | 2 2 1 0 0 | 1 2 4 1 0 | 1 2 2
. x . . . & | 2 | * 720 | 1 1 0 1 1 | 1 2 1 1 1 | 2 1 1
-------------+-----+---------+--------------------+-------------------+---------
x3x . . . & | 6 | 3 3 | 240 * * * * | 1 1 1 0 0 | 1 1 1
x . . x . & | 4 | 2 2 | * 360 * * * | 0 1 1 1 0 | 1 1 1
x . . . x | 4 | 4 0 | * * 90 * * | 0 0 4 0 0 | 0 2 2
. x3o . . & | 3 | 0 3 | * * * 240 * | 1 0 0 1 1 | 2 1 0
. x . x . | 4 | 0 4 | * * * * 180 | 0 2 0 0 1 | 2 0 1
-------------+-----+---------+--------------------+-------------------+---------
x3x3o . . & ♦ 12 | 6 12 | 4 0 0 4 0 | 60 * * * * | 1 1 0
x3x . x . & ♦ 12 | 6 12 | 2 3 0 0 3 | * 120 * * * | 1 0 1
x3x . . x & ♦ 12 | 12 6 | 2 3 3 0 0 | * * 120 * * | 0 1 1
x . o3x . & ♦ 6 | 3 6 | 0 3 0 2 0 | * * * 120 * | 1 1 0
. x3o3x . ♦ 12 | 0 24 | 0 0 0 8 6 | * * * * 30 | 2 0 0
-------------+-----+---------+--------------------+-------------------+---------
x3x3o3x . & ♦ 60 | 30 120 | 20 30 0 40 30 | 5 10 0 10 5 | 12 * *
x3x3o . x & ♦ 24 | 24 24 | 8 12 6 8 0 | 2 0 4 4 0 | * 30 *
x3x . x3x ♦ 36 | 36 36 | 12 18 9 0 9 | 0 6 6 0 0 | * * 20
xxxux3xxxoo3ooxxx3xuxxx&#xt → all heights = sqrt(4/5) = 0.774597
(prip || pseudo (x,x,u)-prip || pseudo gippid || pseudo inv. (x,x,u)-prip || inv. prip)
o....3o....3o....3o.... & | 120 * * | 1 2 2 1 0 0 0 0 0 | 2 2 1 2 1 1 2 2 0 0 0 0 0 0 0 0 | 1 2 1 1 2 2 1 2 1 0 0 0 0 0 | 1 1 2 1 1
.o...3.o...3.o...3.o... & | * 120 * | 0 0 0 1 1 2 2 0 0 | 0 0 0 0 0 1 2 2 2 1 2 2 1 0 0 0 | 0 0 0 0 2 2 1 2 1 1 2 2 1 0 | 0 1 2 1 2
..o..3..o..3..o..3..o.. | * * 120 | 0 0 0 0 0 0 2 2 2 | 0 0 0 0 0 0 0 2 0 0 2 2 2 2 2 1 | 0 0 0 0 0 2 0 2 2 0 2 2 1 2 | 0 0 2 2 2
------------------------------+-------------+-----------------------------------+------------------------------------------------------+-------------------------------------------+--------------
x.... ..... ..... ..... & | 2 0 0 | 60 * * * * * * * * | 2 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | 1 2 1 0 2 2 0 0 0 0 0 0 0 0 | 1 1 2 1 0
..... x.... ..... ..... & | 2 0 0 | * 120 * * * * * * * | 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 1 0 1 1 0 1 1 0 0 0 0 0 0 | 1 1 1 0 1
..... ..... ..... x.... & | 2 0 0 | * * 120 * * * * * * | 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 | 0 1 1 1 0 1 0 1 1 0 0 0 0 0 | 1 0 1 1 1
oo...3oo...3oo...3oo...&#x & | 1 1 0 | * * * 120 * * * * * | 0 0 0 0 0 1 2 2 0 0 0 0 0 0 0 0 | 0 0 0 0 2 2 1 2 1 0 0 0 0 0 | 0 1 2 1 1
.x... ..... ..... ..... & | 0 2 0 | * * * * 60 * * * * | 0 0 0 0 0 1 0 0 2 0 2 0 0 0 0 0 | 0 0 0 0 2 2 0 0 0 1 2 1 0 0 | 0 1 2 1 1
..... .x... ..... ..... & | 0 2 0 | * * * * * 120 * * * | 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 | 0 0 0 0 1 0 1 1 0 1 1 0 1 0 | 0 1 1 0 2
.oo..3.oo..3.oo..3.oo..&#x & | 0 1 1 | * * * * * * 240 * * | 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 | 0 0 0 0 0 1 0 1 1 0 1 1 1 0 | 0 0 1 1 2
..x.. ..... ..... ..... & | 0 0 2 | * * * * * * * 120 * | 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 1 | 0 0 0 0 0 2 0 1 1 0 1 1 0 2 | 0 0 2 2 1
..... ..x.. ..... ..... & | 0 0 2 | * * * * * * * * 120 | 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 | 0 0 0 0 0 0 0 1 1 0 1 1 1 1 | 0 0 1 1 2
------------------------------+-------------+-----------------------------------+------------------------------------------------------+-------------------------------------------+--------------
x....3x.... ..... ..... & | 6 0 0 | 3 3 0 0 0 0 0 0 0 | 40 * * * * * * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0
x.... ..... ..... x.... & | 4 0 0 | 2 0 2 0 0 0 0 0 0 | * 60 * * * * * * * * * * * * * * | 0 1 1 0 0 1 0 0 0 0 0 0 0 0 | 1 0 1 1 0
..... x....3o.... ..... & | 3 0 0 | 0 3 0 0 0 0 0 0 0 | * * 40 * * * * * * * * * * * * * | 1 0 0 1 0 0 1 0 0 0 0 0 0 0 | 1 1 0 0 1
..... x.... ..... x.... & | 4 0 0 | 0 2 2 0 0 0 0 0 0 | * * * 60 * * * * * * * * * * * * | 0 1 0 1 0 0 0 1 0 0 0 0 0 0 | 1 0 1 0 1
..... ..... o....3x.... & | 3 0 0 | 0 0 3 0 0 0 0 0 0 | * * * * 40 * * * * * * * * * * * | 0 0 1 1 0 0 0 0 1 0 0 0 0 0 | 1 0 0 1 1
xx... ..... ..... .....&#x & | 2 2 0 | 1 0 0 2 1 0 0 0 0 | * * * * * 60 * * * * * * * * * * | 0 0 0 0 2 2 0 0 0 0 0 0 0 0 | 0 1 2 1 0
..... xx... ..... .....&#x & | 2 2 0 | 0 1 0 2 0 1 0 0 0 | * * * * * * 120 * * * * * * * * * | 0 0 0 0 1 0 1 1 0 0 0 0 0 0 | 0 1 1 0 1
..... ..... ..... xux..&#x & | 2 2 2 | 0 0 1 2 0 0 2 1 0 | * * * * * * * 120 * * * * * * * * | 0 0 0 0 0 1 0 1 1 0 0 0 0 0 | 0 0 1 1 1
.x...3.x... ..... ..... & | 0 6 0 | 0 0 0 0 3 3 0 0 0 | * * * * * * * * 40 * * * * * * * | 0 0 0 0 1 0 0 0 0 1 1 0 0 0 | 0 1 1 0 1
..... .x...3.o... ..... & | 0 3 0 | 0 0 0 0 0 3 0 0 0 | * * * * * * * * * 40 * * * * * * | 0 0 0 0 0 0 1 0 0 1 0 0 1 0 | 0 1 0 0 2
.xx.. ..... ..... .....&#x & | 0 2 2 | 0 0 0 0 1 0 2 1 0 | * * * * * * * * * * 120 * * * * * | 0 0 0 0 0 1 0 0 0 0 1 1 0 0 | 0 0 1 1 1
..... .xx.. ..... .....&#x & | 0 2 2 | 0 0 0 0 0 1 2 0 1 | * * * * * * * * * * * 120 * * * * | 0 0 0 0 0 0 0 1 0 0 1 0 1 0 | 0 0 1 0 2
..... ..... .ox.. .....&#x & | 0 1 2 | 0 0 0 0 0 0 2 0 1 | * * * * * * * * * * * * 120 * * * | 0 0 0 0 0 0 0 0 1 0 0 1 1 0 | 0 0 0 1 2
..x..3..x.. ..... ..... & | 0 0 6 | 0 0 0 0 0 0 0 3 3 | * * * * * * * * * * * * * 40 * * | 0 0 0 0 0 0 0 0 1 0 1 0 0 1 | 0 0 1 1 1
..x.. ..... ..x.. ..... & | 0 0 4 | 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * * 60 * | 0 0 0 0 0 0 0 1 0 0 0 1 0 1 | 0 0 1 1 1
..x.. ..... ..... ..x.. | 0 0 4 | 0 0 0 0 0 0 0 4 0 | * * * * * * * * * * * * * * * 30 | 0 0 0 0 0 2 0 0 0 0 0 0 0 2 | 0 0 2 2 0
------------------------------+-------------+-----------------------------------+------------------------------------------------------+-------------------------------------------+--------------
x....3x....3o.... ..... & ♦ 12 0 0 | 6 12 0 0 0 0 0 0 0 | 4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 | 10 * * * * * * * * * * * * * | 1 1 0 0 0
x....3x.... ..... x.... & ♦ 12 0 0 | 6 6 6 0 0 0 0 0 0 | 2 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 | * 20 * * * * * * * * * * * * | 1 0 1 0 0
x.... ..... o....3x.... & ♦ 6 0 0 | 3 0 6 0 0 0 0 0 0 | 0 3 0 0 2 0 0 0 0 0 0 0 0 0 0 0 | * * 20 * * * * * * * * * * * | 1 0 0 1 0
..... x....3o....3x.... & ♦ 12 0 0 | 0 12 12 0 0 0 0 0 0 | 0 0 4 6 4 0 0 0 0 0 0 0 0 0 0 0 | * * * 10 * * * * * * * * * * | 1 0 0 0 1
xx...3xx... ..... .....&#x & ♦ 6 6 0 | 3 3 0 6 3 3 0 0 0 | 1 0 0 0 0 3 3 0 1 0 0 0 0 0 0 0 | * * * * 40 * * * * * * * * * | 0 1 1 0 0
xxx.. ..... ..... xux..&#xt & ♦ 4 4 4 | 2 0 2 4 2 0 4 4 0 | 0 1 0 0 0 2 0 2 0 0 2 0 0 0 0 1 | * * * * * 60 * * * * * * * * | 0 0 1 1 0
..... xx...3oo... .....&#x & ♦ 3 3 0 | 0 3 0 3 0 3 0 0 0 | 0 0 1 0 0 0 3 0 0 1 0 0 0 0 0 0 | * * * * * * 40 * * * * * * * | 0 1 0 0 1
..... xxx.. ..... xux..&#xt & ♦ 4 4 4 | 0 2 2 4 0 2 4 2 2 | 0 0 0 1 0 0 2 2 0 0 0 2 0 0 1 0 | * * * * * * * 60 * * * * * * | 0 0 1 0 1
..... ..... oox..3xux..&#xt & ♦ 3 3 6 | 0 0 3 3 0 0 6 3 3 | 0 0 0 0 1 0 0 3 0 0 0 0 3 1 0 0 | * * * * * * * * 40 * * * * * | 0 0 0 1 1
.x...3.x...3.o... ..... & ♦ 0 12 0 | 0 0 0 0 6 12 0 0 0 | 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 | * * * * * * * * * 10 * * * * | 0 1 0 0 1
.xx..3.xx.. ..... .....&#x & ♦ 0 6 6 | 0 0 0 0 3 3 6 3 3 | 0 0 0 0 0 0 0 0 1 0 3 3 0 1 0 0 | * * * * * * * * * * 40 * * * | 0 0 1 0 1
.xx.. ..... .ox.. .....&#x & ♦ 0 2 4 | 0 0 0 0 1 0 4 2 2 | 0 0 0 0 0 0 0 0 0 0 2 0 2 0 1 0 | * * * * * * * * * * * 60 * * | 0 0 0 1 1
..... .xxo.3.oxx. .....&#xt ♦ 0 6 6 | 0 0 0 0 0 6 12 0 6 | 0 0 0 0 0 0 0 0 0 2 0 6 6 0 0 0 | * * * * * * * * * * * * 20 * | 0 0 0 0 2
..x..3..x.. ..... ..x.. & ♦ 0 0 12 | 0 0 0 0 0 0 0 12 6 | 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 3 | * * * * * * * * * * * * * 20 | 0 0 1 1 0
------------------------------+-------------+-----------------------------------+------------------------------------------------------+-------------------------------------------+--------------
x....3x....3o....3x.... & ♦ 60 0 0 | 30 60 60 0 0 0 0 0 0 | 20 30 20 30 20 0 0 0 0 0 0 0 0 0 0 0 | 5 10 10 5 0 0 0 0 0 0 0 0 0 0 | 2 * * * *
xx...3xx...3oo... .....&#x & ♦ 12 12 0 | 6 12 0 12 6 12 0 0 0 | 4 0 4 0 0 6 12 0 4 4 0 0 0 0 0 0 | 1 0 0 0 4 0 4 0 0 1 0 0 0 0 | * 10 * * *
xxx..3xxx.. ..... xux..&#xt & ♦ 12 12 12 | 6 6 6 12 6 6 12 12 6 | 2 3 0 3 0 6 6 6 2 0 6 6 0 2 3 3 | 0 1 0 0 2 3 0 3 0 0 2 0 0 1 | * * 20 * *
xxx.. ..... oox..3xux..&#xt & ♦ 6 6 12 | 3 0 6 6 3 0 12 12 6 | 0 3 0 0 2 3 0 6 0 0 6 0 6 2 3 3 | 0 0 1 0 0 3 0 0 2 0 0 3 0 1 | * * * 20 *
..... xxxo.3ooxx.3xuxx.&#xt & ♦ 12 24 24 | 0 12 12 12 6 24 48 12 24 | 0 0 4 6 4 0 12 12 4 8 12 24 24 4 6 0 | 0 0 0 1 0 0 4 6 4 1 4 6 4 0 | * * * * 10