Acronym sirhin
Name small rhombated hemipenteract,
cantellated demipenteract,
runcic penteract
Circumradius sqrt(21/8) = 1.620185
Lace city
in approx. ASCII-art
x3o3o  x3x3o  o3x3x  o3o3x
                          
                          
                          
x3x3o  u3o3x  x3o3u  o3x3x
                          
                          
                          
o3x3x  x3o3u  u3o3x  x3x3o
                          
                          
                          
o3o3x  o3x3x  x3x3o  x3o3o
Coordinates (3/sqrt(8), 3/sqrt(8), 1/sqrt(8), 1/sqrt(8), 1/sqrt(8))     & all permutations, all even changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polyteral members:
by cells: garpop rap rit ripdip srip
kafandoh 1600160
sirhin 01610016
& others)
Confer
related segmentotera:
ritag thex   thexag thex   teta tuttip  
general polytopal classes:
partial Stott expansions  
External
links
wikipedia

Incidence matrix according to Dynkin symbol

x3o3o *b3x3o

. . .    . . | 160 |   3   6 |   3   6   6   3 |  1  6  3  2  3 |  2  3  1
-------------+-----+---------+-----------------+----------------+---------
x . .    . . |   2 | 240   * |   2   2   0   0 |  1  4  1  0  0 |  2  2  0
. . .    x . |   2 |   * 480 |   0   1   2   1 |  0  2  1  1  2 |  1  2  1
-------------+-----+---------+-----------------+----------------+---------
x3o .    . . |   3 |   3   0 | 160   *   *   * |  1  2  0  0  0 |  2  1  0
x . .    x . |   4 |   2   2 |   * 240   *   * |  0  2  1  0  0 |  1  2  0
. o . *b3x . |   3 |   0   3 |   *   * 320   * |  0  1  0  1  1 |  1  1  1
. . .    x3o |   3 |   0   3 |   *   *   * 160 |  0  0  1  0  2 |  0  2  1
-------------+-----+---------+-----------------+----------------+---------
x3o3o    . .    4 |   6   0 |   4   0   0   0 | 40  *  *  *  * |  2  0  0
x3o . *b3x .   12 |  12  12 |   4   6   4   0 |  * 80  *  *  * |  1  1  0
x . .    x3o    6 |   3   6 |   0   3   0   2 |  *  * 80  *  * |  0  2  0
. o3o *b3x .    4 |   0   6 |   0   0   4   0 |  *  *  * 80  * |  1  0  1
. o . *b3x3o    6 |   0  12 |   0   0   4   4 |  *  *  *  * 80 |  0  1  1
-------------+-----+---------+-----------------+----------------+---------
x3o3o *b3x .   32 |  48  48 |  32  24  32   0 |  8  8  0  8  0 | 10  *  *
x3o . *b3x3o   30 |  30  60 |  10  30  20  20 |  0  5 10  0  5 |  * 16  *
. o3o *b3x3o   10 |   0  30 |   0   0  20  10 |  0  0  0  5  5 |  *  * 16

o3x3o3o4s

demi( . . . . . ) | 160 |   6   3 |   3   6   6   3 |  3  2  3  1  6 |  1  2  3
------------------+-----+---------+-----------------+----------------+---------
demi( . x . . . ) |   2 | 480   * |   1   2   1   0 |  2  1  1  0  2 |  1  1  2
      . . . o4s   |   2 |   * 240 |   0   0   2   2 |  0  0  1  1  4 |  0  2  2
------------------+-----+---------+-----------------+----------------+---------
demi( o3x . . . ) |   3 |   3   0 | 160   *   *   * |  2  0  1  0  0 |  1  0  2
demi( . x3o . . ) |   3 |   3   0 |   * 320   *   * |  1  1  0  0  1 |  1  1  1
      . x 2 o4s   |   4 |   2   2 |   *   * 240   * |  0  0  1  0  2 |  0  1  2
sefa( . . o3o4s ) |   3 |   0   3 |   *   *   * 160 |  0  0  0  1  2 |  0  2  1
------------------+-----+---------+-----------------+----------------+---------
demi( o3x3o . . )    6 |  12   0 |   4   4   0   0 | 80  *  *  *  * |  1  0  1
demi( . x3o3o . )    4 |   6   0 |   0   4   0   0 |  * 80  *  *  * |  1  1  0
      o3x 2 o4s      6 |   6   3 |   2   0   3   0 |  *  * 80  *  * |  0  0  2
      . . o3o4s      4 |   0   6 |   0   0   0   4 |  *  *  * 40  * |  0  2  0
sefa( . x3o3o4s )   12 |  12  12 |   0   4   6   4 |  *  *  *  * 80 |  0  1  1
------------------+-----+---------+-----------------+----------------+---------
demi( o3x3o3o . )   10 |  30   0 |  10  20   0   0 |  5  5  0  0  0 | 16  *  *
      . x3o3o4s     32 |  48  48 |   0  32  24  32 |  0  8  0  8  8 |  * 10  *
sefa( o3x3o3o4s )   30 |  60  30 |  20  20  30  10 |  5  0 10  0  5 |  *  * 16

starting figure: o3x3o3o4x

xxoo3oxxo3ooxx *b3xoox&#xt   → all heights = 1/sqrt(2) = 0.707107
(rit || gyro thex || thex || gyro rit)

o...3o...3o... *b3o...     & | 64  * |  3  3   3  0   0  0 |  3  3  3  3   3  3  0  0  0  0 |  1  3  1  3  3  1  3  0  0  0 | 1 1  3  1
.o..3.o..3.o.. *b3.o..     & |  * 96 |  0  0   2  1   4  2 |  0  0  0  2   1  1  2  2  3  4 |  0  0  0  6  1  2  2  1  1  2 | 0 2  3  1
-----------------------------+-------+---------------------+--------------------------------+-------------------------------+----------
x... .... ....    ....     & |  2  0 | 96  *   *  *   *  * |  2  1  0  1   0  0  0  0  0  0 |  1  2  0  2  1  0  0  0  0  0 | 1 1  2  0
.... .... ....    x...     & |  2  0 |  * 96   *  *   *  * |  0  1  2  0   0  1  0  0  0  0 |  0  2  1  0  1  0  2  0  0  0 | 1 0  2  1
oo..3oo..3oo.. *b3oo..&#x  & |  1  1 |  *  * 192  *   *  * |  0  0  0  1   2  1  0  0  0  0 |  0  0  0  2  1  1  2  0  0  0 | 0 1  2  1
.x.. .... ....    ....     & |  0  2 |  *  *   * 48   *  * |  0  0  0  2   0  0  0  0  2  0 |  0  0  0  4  1  0  0  0  1  0 | 0 2  2  0
.... .x.. ....    ....     & |  0  2 |  *  *   *  * 192  * |  0  0  0  0   1  0  1  1  0  1 |  0  0  0  2  0  1  1  1  0  1 | 0 1  2  1
.oo.3.oo.3.oo. *b3.oo.&#x    |  0  2 |  *  *   *  *   * 96 |  0  0  0  0   0  0  0  0  2  2 |  0  0  0  4  0  0  0  0  1  1 | 0 2  2  0
-----------------------------+-------+---------------------+--------------------------------+-------------------------------+----------
x...3o... ....    ....     & |  3  0 |  3  0   0  0   0  0 | 64  *  *  *   *  *  *  *  *  * |  1  1  0  1  0  0  0  0  0  0 | 1 1  1  0
x... .... ....    x...     & |  4  0 |  2  2   0  0   0  0 |  * 48  *  *   *  *  *  *  *  * |  0  2  0  0  1  0  0  0  0  0 | 1 0  2  0
.... o... .... *b3x...     & |  3  0 |  0  3   0  0   0  0 |  *  * 64  *   *  *  *  *  *  * |  0  1  1  0  0  0  1  0  0  0 | 1 0  1  1
xx.. .... ....    ....&#x  & |  2  2 |  1  0   2  1   0  0 |  *  *  * 96   *  *  *  *  *  * |  0  0  0  2  1  0  0  0  0  0 | 0 1  2  0
.... ox.. ....    ....&#x  & |  1  2 |  0  0   2  0   1  0 |  *  *  *  * 192  *  *  *  *  * |  0  0  0  1  0  1  1  0  0  0 | 0 1  1  1
.... .... ....    xo..&#x  & |  2  1 |  0  1   2  0   0  0 |  *  *  *  *   * 96  *  *  *  * |  0  0  0  0  1  0  2  0  0  0 | 0 0  2  1
.... .x..3.o..    ....     & |  0  3 |  0  0   0  0   3  0 |  *  *  *  *   *  * 64  *  *  * |  0  0  0  1  0  1  0  1  0  0 | 0 1  1  1
.... .x.. .... *b3.o..     & |  0  3 |  0  0   0  0   3  0 |  *  *  *  *   *  *  * 64  *  * |  0  0  0  0  0  0  1  1  0  1 | 0 0  2  1
.xo. .... ....    ....&#x  & |  0  3 |  0  0   0  1   0  2 |  *  *  *  *   *  *  *  * 96  * |  0  0  0  2  0  0  0  0  1  0 | 0 2  1  0
.... .xx. ....    ....&#x    |  0  4 |  0  0   0  0   2  2 |  *  *  *  *   *  *  *  *  * 96 |  0  0  0  2  0  0  0  0  0  1 | 0 1  2  0
-----------------------------+-------+---------------------+--------------------------------+-------------------------------+----------
x...3o...3o...    ....     &   4  0 |  6  0   0  0   0  0 |  4  0  0  0   0  0  0  0  0  0 | 16  *  *  *  *  *  *  *  *  * | 1 1  0  0
x...3o... .... *b3x...     &  12  0 | 12 12   0  0   0  0 |  4  6  4  0   0  0  0  0  0  0 |  * 16  *  *  *  *  *  *  *  * | 1 0  1  0
.... o...3o... *b3x...     &   4  0 |  0  6   0  0   0  0 |  0  0  4  0   0  0  0  0  0  0 |  *  * 16  *  *  *  *  *  *  * | 1 0  0  1
xxo.3oxx. ....    ....&#xt &   3  9 |  3  0   6  3   6  6 |  1  0  0  3   3  0  1  0  3  3 |  *  *  * 64  *  *  *  *  *  * | 0 1  1  0
xx.. .... ....    xo..&#x  &   4  2 |  2  2   4  1   0  0 |  0  1  0  2   0  2  0  0  0  0 |  *  *  *  * 48  *  *  *  *  * | 0 0  2  0
.... ox..3oo..    ....&#x  &   1  3 |  0  0   3  0   3  0 |  0  0  0  0   3  0  1  0  0  0 |  *  *  *  *  * 64  *  *  *  * | 0 1  0  1
.... ox.. .... *b3xo..&#x  &   3  3 |  0  3   6  0   3  0 |  0  0  1  0   3  3  0  1  0  0 |  *  *  *  *  *  * 64  *  *  * | 0 0  1  1
.... .x..3.o.. *b3.o..     &   0  6 |  0  0   0  0  12  0 |  0  0  0  0   0  0  4  4  0  0 |  *  *  *  *  *  *  * 16  *  * | 0 0  1  1
.xo. .... .ox.    ....&#x      0  4 |  0  0   0  2   0  4 |  0  0  0  0   0  0  0  0  4  0 |  *  *  *  *  *  *  *  * 24  * | 0 2  0  0
.... .xx. .... *b3.oo.&#x      0  6 |  0  0   0  0   6  3 |  0  0  0  0   0  0  0  2  0  3 |  *  *  *  *  *  *  *  *  * 32 | 0 0  2  0
-----------------------------+-------+---------------------+--------------------------------+-------------------------------+----------
x...3o...3o... *b3x...     &  32  0 | 48 48   0  0   0  0 | 32 24 32  0   0  0  0  0  0  0 |  8  8  8  0  0  0  0  0  0  0 | 2 *  *  *
xxoo3oxxo3ooxx    ....&#xt     8 24 | 12  0  24 12  24 24 |  8  0  0 12  24  0  8  0 24 12 |  2  0  0  8  0  8  0  0  6  0 | * 8  *  *
xxo.3oxx. .... *b3xoo.&#xt &  12 18 | 12 12  24  6  24 12 |  4  6  4 12  12 12  4  8  6 12 |  0  1  0  4  6  0  4  1  0  4 | * * 16  *
.... ox..3oo.. *b3xo..&#x  &   4  6 |  0  6  12  0  12  0 |  0  0  4  0  12  6  4  4  0  0 |  0  0  1  0  0  4  4  1  0  0 | * *  * 16

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