Acronym pirhin
Name prismatorhombated hemipenteract,
runcicantellated demipenteract,
steriruncic penteract
Circumradius sqrt(37/8) = 2.150581
Lace city
in approx. ASCII-art
 ©  
       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)
Coordinates (5 sqrt(2)/4, 3 sqrt(2)/4, sqrt(2)/4, sqrt(2)/4, sqrt(2)/4)   & all permutations, all changes of sign
Confer
related segmentotera:
taha
general polytopal classes:
lace simplices   partial Stott expansions  
External
links
wikipedia   polytopewiki

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

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