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Acronym
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pirhin
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Name
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prismatorhombated hemipenteract,
runcicantellated demipenteract,
steriruncic penteract
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Circumradius
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sqrt(37/8) = 2.150581
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Lace city
in approx. ASCII-art
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 ©
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o3o3x o3x3x x3x3o x3o3o -- o3o3x *b3x (rit)
o3o3x o3u3x x3u3o x3o3o -- o3o3x *b3u ((x,u)-rit)
o3x3x o3u3x x3x3u u3x3x x3u3o x3x3o -- o3x3x *b3x (tah)
x3x3o x3u3o u3x3x x3x3u o3u3x o3x3x -- x3x3o *b3x (gyro tah)
x3o3o x3u3o o3u3x o3o3x -- x3o3o *b3u (gyro (x,u)-rit)
x3o3o x3x3o o3x3x o3o3x -- x3o3o *b3x (gyro rit)
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Coordinates
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(5 sqrt(2)/4, 3 sqrt(2)/4, sqrt(2)/4, sqrt(2)/4, sqrt(2)/4) & all permutations, all changes of sign
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Face vector
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320, 1120, 1280, 560, 82
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Confer
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- related segmentotera:
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taha
- general polytopal classes:
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Wythoffian polytera
lace simplices
partial Stott expansions
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External
links
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Incidence matrix according to Dynkin symbol
x3o3o *b3x3x
. . . . . | 320 | 3 3 1 | 3 3 3 3 3 | 1 3 3 3 1 3 | 1 1 3 1
-------------+-----+-------------+---------------------+--------------------+------------
x . . . . | 2 | 480 * * | 2 1 1 0 0 | 1 2 2 1 0 0 | 1 1 2 0
. . . x . | 2 | * 480 * | 0 1 0 2 1 | 0 2 0 1 1 2 | 1 0 2 1
. . . . x | 2 | * * 160 | 0 0 3 0 3 | 0 0 3 3 0 3 | 0 1 3 1
-------------+-----+-------------+---------------------+--------------------+------------
x3o . . . | 3 | 3 0 0 | 320 * * * * | 1 1 1 0 0 0 | 1 1 1 0
x . . x . | 4 | 2 2 0 | * 240 * * * | 0 2 0 1 0 0 | 1 0 2 0
x . . . x | 4 | 2 0 2 | * * 240 * * | 0 0 2 1 0 0 | 0 1 2 0
. o . *b3x . | 3 | 0 3 0 | * * * 320 * | 0 1 0 0 1 1 | 1 0 1 1
. . . x3x | 6 | 0 3 3 | * * * * 160 | 0 0 0 1 0 2 | 0 0 2 1
-------------+-----+-------------+---------------------+--------------------+------------
x3o3o . . ♦ 4 | 6 0 0 | 4 0 0 0 0 | 80 * * * * * | 1 1 0 0
x3o . *b3x . ♦ 12 | 12 12 0 | 4 6 0 4 0 | * 80 * * * * | 1 0 1 0
x3o . . x ♦ 6 | 6 0 3 | 2 0 3 0 0 | * * 160 * * * | 0 1 1 0
x . . x3x ♦ 12 | 6 6 6 | 0 3 3 0 2 | * * * 80 * * | 0 0 2 0
. o3o *b3x . ♦ 4 | 0 6 0 | 0 0 0 4 0 | * * * * 80 * | 1 0 0 1
. o . *b3x3x ♦ 12 | 0 12 6 | 0 0 0 4 4 | * * * * * 80 | 0 0 1 1
-------------+-----+-------------+---------------------+--------------------+------------
x3o3o *b3x . ♦ 32 | 48 48 0 | 32 24 0 32 0 | 8 8 0 0 8 0 | 10 * * *
x3o3o . x ♦ 8 | 12 0 4 | 8 0 6 0 0 | 2 0 4 0 0 0 | * 40 * *
x3o . *b3x3x ♦ 60 | 60 60 30 | 20 30 30 20 20 | 0 5 10 10 0 5 | * * 16 *
. o3o *b3x3x ♦ 20 | 0 30 10 | 0 0 0 20 10 | 0 0 0 0 5 5 | * * * 16
x3x3o3o4s
demi( . . . . . ) | 320 | 1 3 3 | 3 3 3 3 3 | 3 1 3 1 3 3 | 1 1 1 3
------------------+-----+-------------+---------------------+--------------------+------------
demi( x . . . . ) | 2 | 160 * * | 3 0 3 0 0 | 3 0 3 0 3 0 | 1 1 0 3
demi( . x . . . ) | 2 | * 480 * | 1 2 0 1 0 | 2 1 1 0 0 2 | 1 0 1 2
. . . o4s | 2 | * * 480 | 0 0 1 1 2 | 0 0 1 1 2 2 | 0 1 1 2
------------------+-----+-------------+---------------------+--------------------+------------
demi( x3x . . . ) | 6 | 3 3 0 | 160 * * * * | 2 0 1 0 0 0 | 1 0 0 2
demi( . x3o . . ) | 3 | 0 3 0 | * 320 * * * | 1 1 0 0 0 1 | 1 0 1 1
x . 2 o4s | 4 | 2 0 2 | * * 240 * * | 0 0 1 0 2 0 | 0 1 0 2
. x 2 o4s | 4 | 0 2 2 | * * * 240 * | 0 0 1 0 0 2 | 0 0 1 2
sefa( . . o3o4s ) | 3 | 0 0 3 | * * * * 320 | 0 0 0 1 1 1 | 0 1 1 1
------------------+-----+-------------+---------------------+--------------------+------------
demi( x3x3o . . ) ♦ 12 | 6 12 0 | 4 4 0 0 0 | 80 * * * * * | 1 0 0 1
demi( . x3o3o . ) ♦ 4 | 0 6 0 | 0 4 0 0 0 | * 80 * * * * | 1 0 1 0
x3x 2 o4s ♦ 12 | 6 6 6 | 2 0 3 3 0 | * * 80 * * * | 0 0 0 2
. . o3o4s ♦ 4 | 0 0 6 | 0 0 0 0 4 | * * * 80 * * | 0 1 1 0
sefa( x 2 o3o4s ) ♦ 6 | 3 0 6 | 0 0 3 0 2 | * * * * 160 * | 0 1 0 1
sefa( . x3o3o4s ) ♦ 12 | 0 12 12 | 0 4 0 6 4 | * * * * * 80 | 0 0 1 1
------------------+-----+-------------+---------------------+--------------------+------------
demi( x3x3o3o . ) ♦ 20 | 10 30 0 | 10 20 0 0 0 | 5 5 0 0 0 0 | 16 * * *
x 2 o3o4s ♦ 8 | 4 0 12 | 0 0 6 0 8 | 0 0 0 2 4 0 | * 40 * *
. x3o3o4s ♦ 32 | 0 48 48 | 0 32 0 24 32 | 0 8 0 8 0 8 | * * 10 *
sefa( x3x3o3o4s ) ♦ 60 | 30 60 60 | 20 20 30 30 20 | 5 0 10 0 10 5 | * * * 16
starting figure: x3x3o3o4x
oooxxx3ooxxoo3xxxooo *b3xuxxux&#xt → all heights = 1/sqrt(2) = 0.707107
o.....3o.....3o..... *b3o..... & | 64 * * | 3 3 1 0 0 0 0 0 0 | 3 3 3 3 3 0 0 0 0 0 0 0 0 0 | 1 1 3 3 3 3 0 0 0 0 0 0 0 | 1 1 1 3 0 0
.o....3.o....3.o.... *b3.o.... & | * 64 * | 0 0 1 3 3 0 0 0 0 | 0 0 0 3 3 3 3 3 0 0 0 0 0 0 | 0 0 0 3 3 3 1 1 3 0 0 0 0 | 0 1 1 3 1 0
..o...3..o...3..o... *b3..o... & | * * 192 | 0 0 0 0 1 2 1 1 2 | 0 0 0 0 1 0 2 1 1 2 1 3 2 2 | 0 0 0 0 2 1 0 1 3 1 1 3 2 | 0 0 1 3 1 1
-------------------------------------+-----------+-------------------------------+---------------------------------------------+----------------------------------------+----------------
...... ...... x..... ...... & | 2 0 0 | 96 * * * * * * * * | 2 0 1 1 0 0 0 0 0 0 0 0 0 0 | 1 0 2 2 0 1 0 0 0 0 0 0 0 | 1 1 0 2 0 0
...... ...... ...... x..... & | 2 0 0 | * 96 * * * * * * * | 0 2 1 0 1 0 0 0 0 0 0 0 0 0 | 0 1 2 0 2 1 0 0 0 0 0 0 0 | 1 0 1 2 0 0
oo....3oo....3oo.... oo....&#x & | 1 1 0 | * * 64 * * * * * * | 0 0 0 3 3 0 0 0 0 0 0 0 0 0 | 0 0 0 3 3 3 0 0 0 0 0 0 0 | 0 1 1 3 0 0
...... ...... .x.... ...... & | 0 2 0 | * * * 96 * * * * * | 0 0 0 1 0 2 0 1 0 0 0 0 0 0 | 0 0 0 2 0 1 1 0 2 0 0 0 0 | 0 1 0 2 1 0
.oo...3.oo...3.oo... .oo...&#x & | 0 1 1 | * * * * 192 * * * * | 0 0 0 0 1 0 2 1 0 0 0 0 0 0 | 0 0 0 0 2 1 0 1 2 0 0 0 0 | 0 0 1 2 1 0
...... ..x... ...... ...... & | 0 0 2 | * * * * * 192 * * * | 0 0 0 0 0 0 1 0 1 1 0 0 1 0 | 0 0 0 0 1 0 0 1 2 1 0 0 1 | 0 0 1 2 1 0
...... ...... ..x... ...... & | 0 0 2 | * * * * * * 96 * * | 0 0 0 0 0 0 0 1 0 0 1 2 0 0 | 0 0 0 0 0 1 0 0 2 0 1 2 0 | 0 0 0 2 1 1
...... ...... ...... ..x... & | 0 0 2 | * * * * * * * 96 * | 0 0 0 0 1 0 0 0 0 2 1 0 0 2 | 0 0 0 0 2 1 0 0 0 1 0 3 2 | 0 0 1 3 0 1
..oo..3..oo..3..oo.. ..oo..&#x | 0 0 2 | * * * * * * * * 192 | 0 0 0 0 0 0 0 0 0 0 0 2 1 1 | 0 0 0 0 0 0 0 0 2 0 1 2 1 | 0 0 0 2 1 1
-------------------------------------+-----------+-------------------------------+---------------------------------------------+----------------------------------------+----------------
...... o.....3x..... ...... & | 3 0 0 | 3 0 0 0 0 0 0 0 0 | 64 * * * * * * * * * * * * * | 1 0 1 1 0 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0
...... o..... ...... *b3x..... & | 3 0 0 | 0 3 0 0 0 0 0 0 0 | * 64 * * * * * * * * * * * * | 0 1 1 0 1 0 0 0 0 0 0 0 0 | 1 0 1 1 0 0
...... ...... x..... x..... & | 4 0 0 | 2 2 0 0 0 0 0 0 0 | * * 48 * * * * * * * * * * * | 0 0 2 0 0 1 0 0 0 0 0 0 0 | 1 0 0 2 0 0
...... ...... xx.... ......&#x & | 2 2 0 | 1 0 2 1 0 0 0 0 0 | * * * 96 * * * * * * * * * * | 0 0 0 2 0 1 0 0 0 0 0 0 0 | 0 1 0 2 0 0
...... ...... ...... xux...&#x & | 2 2 2 | 0 1 2 0 2 0 0 1 0 | * * * * 96 * * * * * * * * * | 0 0 0 0 2 1 0 0 0 0 0 0 0 | 0 0 1 2 0 0
...... .o....3.x.... ...... & | 0 3 0 | 0 0 0 3 0 0 0 0 0 | * * * * * 64 * * * * * * * * | 0 0 0 1 0 0 1 0 1 0 0 0 0 | 0 1 0 1 1 0
...... .ox... ...... ......&#x & | 0 1 2 | 0 0 0 0 2 1 0 0 0 | * * * * * * 192 * * * * * * * | 0 0 0 0 1 0 0 1 1 0 0 0 0 | 0 0 1 1 1 0
...... ...... .xx... ......&#x & | 0 2 2 | 0 0 0 1 2 0 1 0 0 | * * * * * * * 96 * * * * * * | 0 0 0 0 0 1 0 0 2 0 0 0 0 | 0 0 0 2 1 0
..o...3..x... ...... ...... & | 0 0 3 | 0 0 0 0 0 3 0 0 0 | * * * * * * * * 64 * * * * * | 0 0 0 0 0 0 0 1 1 1 0 0 0 | 0 0 1 1 1 0
...... ..x... ...... *b3..x... & | 0 0 6 | 0 0 0 0 0 3 0 3 0 | * * * * * * * * * 64 * * * * | 0 0 0 0 1 0 0 0 0 1 0 0 1 | 0 0 1 2 0 0
...... ...... ..x... ..x... & | 0 0 4 | 0 0 0 0 0 0 2 2 0 | * * * * * * * * * * 48 * * * | 0 0 0 0 0 1 0 0 0 0 0 2 0 | 0 0 0 2 0 1
..ox.. ...... ...... ......&#x & | 0 0 3 | 0 0 0 0 0 0 1 0 2 | * * * * * * * * * * * 192 * * | 0 0 0 0 0 0 0 0 1 0 1 1 0 | 0 0 0 1 1 1
...... ..xx.. ...... ......&#x | 0 0 4 | 0 0 0 0 0 2 0 0 2 | * * * * * * * * * * * * 96 * | 0 0 0 0 0 0 0 0 2 0 0 0 1 | 0 0 0 2 1 0
...... ...... ...... ..xx..&#x | 0 0 4 | 0 0 0 0 0 0 0 2 2 | * * * * * * * * * * * * * 96 | 0 0 0 0 0 0 0 0 0 0 0 2 1 | 0 0 0 2 0 1
-------------------------------------+-----------+-------------------------------+---------------------------------------------+----------------------------------------+----------------
o.....3o.....3x..... ...... & ♦ 4 0 0 | 6 0 0 0 0 0 0 0 0 | 4 0 0 0 0 0 0 0 0 0 0 0 0 0 | 16 * * * * * * * * * * * * | 1 1 0 0 0 0
o.....3o..... ...... *b3x..... & ♦ 4 0 0 | 0 6 0 0 0 0 0 0 0 | 0 4 0 0 0 0 0 0 0 0 0 0 0 0 | * 16 * * * * * * * * * * * | 1 0 1 0 0 0
...... o.....3x..... *b3x..... & ♦ 12 0 0 | 12 12 0 0 0 0 0 0 0 | 4 4 6 0 0 0 0 0 0 0 0 0 0 0 | * * 16 * * * * * * * * * * | 1 0 0 1 0 0
...... oo....3xx.... ......&#x & ♦ 3 3 0 | 3 0 3 3 0 0 0 0 0 | 1 0 0 3 0 1 0 0 0 0 0 0 0 0 | * * * 64 * * * * * * * * * | 0 1 0 1 0 0
...... oox... ...... *b3xux...&#xt & ♦ 3 3 6 | 0 3 3 0 6 3 0 3 0 | 0 1 0 0 3 0 3 0 0 1 0 0 0 0 | * * * * 64 * * * * * * * * | 0 0 1 1 0 0
...... ...... xxx... xux...&#xt & ♦ 4 4 4 | 2 2 4 2 4 0 2 2 0 | 0 0 1 2 2 0 0 2 0 0 1 0 0 0 | * * * * * 48 * * * * * * * | 0 0 0 2 0 0
.o....3.o....3.x.... ...... & ♦ 0 4 0 | 0 0 0 6 0 0 0 0 0 | 0 0 0 0 0 4 0 0 0 0 0 0 0 0 | * * * * * * 16 * * * * * * | 0 1 0 0 1 0
.oo...3.ox... ...... ......&#x & ♦ 0 1 3 | 0 0 0 0 3 3 0 0 0 | 0 0 0 0 0 0 3 0 1 0 0 0 0 0 | * * * * * * * 64 * * * * * | 0 0 1 0 1 0
...... .oxx..3.xxo.. ......&#xt & ♦ 0 3 9 | 0 0 0 3 6 6 3 0 6 | 0 0 0 0 0 1 3 3 1 0 0 3 3 0 | * * * * * * * * 64 * * * * | 0 0 0 1 1 0
..o...3..x... ...... *b3..x... & ♦ 0 0 12 | 0 0 0 0 0 12 0 6 0 | 0 0 0 0 0 0 0 0 4 4 0 0 0 0 | * * * * * * * * * 16 * * * | 0 0 1 1 0 0
..ox.. ...... ..xo.. ......&#x & ♦ 0 0 4 | 0 0 0 0 0 0 2 0 4 | 0 0 0 0 0 0 0 0 0 0 0 4 0 0 | * * * * * * * * * * 48 * * | 0 0 0 0 1 1
..ox.. ...... ...... ..xx..&#x & ♦ 0 0 6 | 0 0 0 0 0 0 2 3 4 | 0 0 0 0 0 0 0 0 0 0 1 2 0 2 | * * * * * * * * * * * 96 * | 0 0 0 1 0 1
...... ..xx.. ...... *b3..xx.. ♦ 0 0 12 | 0 0 0 0 0 6 0 6 6 | 0 0 0 0 0 0 0 0 0 2 0 0 3 3 | * * * * * * * * * * * * 32 | 0 0 0 2 0 0
-------------------------------------+-----------+-------------------------------+---------------------------------------------+----------------------------------------+----------------
o.....3o.....3x..... *b3x..... & ♦ 32 0 0 | 48 48 0 0 0 0 0 0 0 | 32 32 24 0 0 0 0 0 0 0 0 0 0 0 | 8 8 8 0 0 0 0 0 0 0 0 0 0 | 2 * * * * *
oo....3oo....3xx.... ......&#x & ♦ 4 4 0 | 6 0 4 6 0 0 0 0 0 | 4 0 0 6 0 4 0 0 0 0 0 0 0 0 | 1 0 0 4 0 0 1 0 0 0 0 0 0 | * 16 * * * *
ooo...3oox... ...... *b3xux...&#xt & ♦ 4 4 12 | 0 6 4 0 12 12 0 6 0 | 0 4 0 0 6 0 12 0 4 4 0 0 0 0 | 0 1 0 0 4 0 0 4 0 1 0 0 0 | * * 16 * * *
...... ooxx..3xxxo.. *b3xuxx..&#xt & ♦ 12 12 36 | 12 12 12 12 24 24 12 18 24 | 4 4 6 12 12 4 12 12 4 8 6 12 12 12 | 0 0 1 4 4 6 0 0 4 1 0 6 4 | * * * 16 * *
.ooxx.3.oxxo.3.xxoo. ......&#x & ♦ 0 8 24 | 0 0 0 12 24 24 12 0 24 | 0 0 0 0 0 8 24 12 8 0 0 24 12 0 | 0 0 0 0 0 0 2 8 8 0 6 0 0 | * * * * 8 *
..ox.. ...... ..xo.. ..xx..&#x ♦ 0 0 8 | 0 0 0 0 0 0 4 4 8 | 0 0 0 0 0 0 0 0 0 0 2 8 0 4 | 0 0 0 0 0 0 0 0 0 0 2 4 0 | * * * * * 24