Acronym sirhax
Name small rhombated hemihexeract,
cantellated demihexeract,
runcic hexeract
Circumradius sqrt(15)/2 = 1.936492
Lace city
in approx. ASCII-art 
 ©
 
r   t   T   R		-- x3o3o *b3x3o (sirhin)
             
t   u   U   T		-- x3x3o *b3o3o (thin)
             
T   U   u   t		-- o3x3x *b3o3o (alt. thin)
             
R   T   t   r		-- o3o3x *b3x3o (alt. sirhin)

where:
r = x3o3o *b3x (rit)
R = o3o3x *b3x (gyro rit)
t = x3x3o *b3o (thex)
T = o3x3o *b3x (gyro thex)
u = u3o3o *b3x ((u,x)-rit)
U = x3o3o *b3u ((x,u)-rit)
Coordinates (3, 3, 3, 1, 1, 1)/sqrt(8)     & all permutations, all even changes of sign
Face vector 640, 3840, 5920, 3520, 876, 76
Confer
related scaliform:
thina  
related segmentopeta:
sirhinathin   thina  
general polytopal classes:
Wythoffian polypeta   lace simplices  
External
links 		wikipedia   polytopewiki  

Incidence matrix according to Dynkin symbol

x3o3o *b3x3o3o

. . .    . . . | 640 |   3    9 |   3    9    9    9 |   1   9   9   3   9   3 |  3   9   3   3   3 |  3  3  1
---------------+-----+----------+--------------------+-------------------------+--------------------+---------
x . .    . . . |   2 | 960    * |   2    3    0    0 |   1   6   3   0   0   0 |  3   6   1   0   0 |  3  2  0
. . .    x . . |   2 |   * 2880 |   0    1    2    2 |   0   2   2   1   4   1 |  1   4   1   2   2 |  2  2  1
---------------+-----+----------+--------------------+-------------------------+--------------------+---------
x3o .    . . . |   3 |   3    0 | 640    *    *    * |   1   3   0   0   0   0 |  3   3   0   0   0 |  3  1  0
x . .    x . . |   4 |   2    2 |   * 1440    *    * |   0   2   2   0   0   0 |  1   4   1   0   0 |  2  2  0
. o . *b3x . . |   3 |   0    3 |   *    * 1920    * |   0   1   0   1   2   0 |  1   2   0   2   1 |  2  1  1
. . .    x3o . |   3 |   0    3 |   *    *    * 1920 |   0   0   1   0   2   1 |  0   2   1   1   2 |  1  2  1
---------------+-----+----------+--------------------+-------------------------+--------------------+---------
x3o3o    . . . ♦   4 |   6    0 |   4    0    0    0 | 160   *   *   *   *   * |  3   0   0   0   0 |  3  0  0
x3o . *b3x . . ♦  12 |  12   12 |   4    6    4    0 |   * 480   *   *   *   * |  1   2   0   0   0 |  2  1  0
x . .    x3o . ♦   6 |   3    6 |   0    3    0    2 |   *   * 960   *   *   * |  0   2   1   0   0 |  1  2  0
. o3o *b3x . . ♦   4 |   0    6 |   0    0    4    0 |   *   *   * 480   *   * |  1   0   0   2   0 |  2  0  1
. o . *b3x3o . ♦   6 |   0   12 |   0    0    4    4 |   *   *   *   * 960   * |  0   1   0   1   1 |  1  1  1
. . .    x3o3o ♦   4 |   0    6 |   0    0    0    4 |   *   *   *   *   * 480 |  0   0   1   0   2 |  0  2  1
---------------+-----+----------+--------------------+-------------------------+--------------------+---------
x3o3o *b3x . . ♦  32 |  48   48 |  32   24   32    0 |   8   8   0   8   0   0 | 60   *   *   *   * |  2  0  0
x3o . *b3x3o . ♦  30 |  30   60 |  10   30   20   20 |   0   5  10   0   5   0 |  * 192   *   *   * |  1  1  0
x . .    x3o3o ♦   8 |   4   12 |   0    6    0    8 |   0   0   4   0   0   2 |  *   * 240   *   * |  0  2  0
. o3o *b3x3o . ♦  10 |   0   30 |   0    0   20   10 |   0   0   0   5   5   0 |  *   *   * 192   * |  1  0  1
. o . *b3x3o3o ♦  10 |   0   30 |   0    0   10   20 |   0   0   0   0   5   5 |  *   *   *   * 192 |  0  1  1
---------------+-----+----------+--------------------+-------------------------+--------------------+---------
x3o3o *b3x3o . ♦ 160 | 240  480 | 160  240  320  160 |  40  80  80  80  80   0 | 10  16   0  16   0 | 12  *  *
x3o . *b3x3o3o ♦  60 |  60  180 |  20   90   60  120 |   0  15  60   0  30  30 |  0   6  15   0   6 |  * 32  *
. o3o *b3x3o3o ♦  20 |   0   90 |   0    0   60   60 |   0   0   0  15  30  15 |  0   0   0   6   6 |  *  * 32


o3o3x3o3o4s

demi( . . . . . . ) | 640 |    9   3 |    9    9    9   3 |   3   9   3   9   1   9 |   3   3   3  3   9 |  1  3  3
--------------------+-----+----------+--------------------+-------------------------+--------------------+---------
demi( . . x . . . ) |   2 | 2880   * |    2    2    1   0 |   1   4   1   2   0   2 |   2   2   1  1   4 |  1  2  2
      . . . . o4s   |   2 |    * 960 |    0    0    3   2 |   0   0   0   3   1   6 |   0   0   1  3   6 |  0  3  2
--------------------+-----+----------+--------------------+-------------------------+--------------------+---------
demi( . o3x . . . ) |   3 |    3   0 | 1920    *    *   * |   1   2   0   1   0   0 |   2   1   1  0   2 |  1  1  2
demi( . . x3o . . ) |   3 |    3   0 |    * 1920    *   * |   0   2   1   0   0   1 |   1   2   0  1   2 |  1  2  1
      . . x 2 o4s   |   4 |    2   2 |    *    * 1440   * |   0   0   0   2   0   2 |   0   0   1  1   4 |  0  2  2
sefa( . . . o3o4s ) |   3 |    0   3 |    *    *    * 640 |   0   0   0   0   1   3 |   0   0   0  3   3 |  0  3  1
--------------------+-----+----------+--------------------+-------------------------+--------------------+---------
demi( o3o3x . . . ) ♦   4 |    6   0 |    4    0    0   0 | 480   *   *   *   *   * |   2   0   1  0   0 |  1  0  2
demi( . o3x3o . . ) ♦   6 |   12   0 |    4    4    0   0 |   * 960   *   *   *   * |   1   1   0  0   1 |  1  1  1
demi( . . x3o3o . ) ♦   4 |    6   0 |    0    4    0   0 |   *   * 480   *   *   * |   0   2   0  1   0 |  1  2  0
      . o3x 2 o4s   ♦   6 |    6   3 |    2    0    3   0 |   *   *   * 960   *   * |   0   0   1  0   2 |  0  1  2
      . . . o3o4s   ♦   4 |    0   6 |    0    0    0   4 |   *   *   *   * 160   * |   0   0   0  3   0 |  0  3  0
sefa( . . x3o3o4s ) ♦  12 |   12  12 |    0    4    6   4 |   *   *   *   *   * 480 |   0   0   0  1   2 |  0  2  1
--------------------+-----+----------+--------------------+-------------------------+--------------------+---------
demi( o3o3x3o . . ) ♦  10 |   30   0 |   20   10    0   0 |   5   5   0   0   0   0 | 192   *   *  *   * |  1  0  1
demi( . o3x3o3o . ) ♦  10 |   30   0 |   10   20    0   0 |   0   5   5   0   0   0 |   * 192   *  *   * |  1  1  0
      o3o3x 2 o4s   ♦   8 |   12   4 |    8    0    6   0 |   2   0   0   4   0   0 |   *   * 240  *   * |  0  0  2
      . . x3o3o4s   ♦  32 |   48  48 |    0   32   24  32 |   0   0   8   0   8   8 |   *   *   * 60   * |  0  2  0
sefa( . o3x3o3o4s ) ♦  30 |   60  30 |   20   20   30  10 |   0   5   0  10   0   5 |   *   *   *  * 192 |  0  1  1
--------------------+-----+----------+--------------------+-------------------------+--------------------+---------
demi( o3o3x3o3o . ) ♦  20 |   90   0 |   60   60    0   0 |  15  30  15   0   0   0 |   6   6   0  0   0 | 32  *  *
      . o3x3o3o4s   ♦ 160 |  480 240 |  160  320  240 160 |   0  80  80  80  40  80 |   0  16   0 10  16 |  * 12  *
sefa( o3o3x3o3o4s ) ♦  60 |  180  60 |  120   60   90  20 |  30  30   0  60   0  15 |   6   0  15  0   6 |  *  * 32

starting figure: o3o3x3o3o4x


xxoo3oxxo3ooxx *b3xoox3oooo&#xt   → all heights = 1/sqrt(2) = 0.707107
(sirhin || thin || alt. thin || alt. sirhin)

o...3o...3o... *b3o...3o...     & | 320   * |   3   6   3   0   0   0 |   3   6   6   3   3   3   6   0   0   0   0 |  1   6   3   2   3   3   6   1   6   3   0   0  0   0 |  2  3  1  1   6   3   2   3  0  0 | 1  2  3  1
.o..3.o..3.o.. *b3.o..3.o..     & |   * 320 |   0   0   3   1   6   2 |   0   0   0   0   3   6   3   3   6   3   6 |  0   0   0   0   0   9   3   3   6   1   3   2  1   6 |  0  0  0  3   9   1   3   2  1  2 | 0  3  3  1
----------------------------------+---------+-------------------------+---------------------------------------------+-------------------------------------------------------+-----------------------------------+-----------
x... .... ....    .... ....     & |   2   0 | 480   *   *   *   *   * |   2   2   0   0   1   0   0   0   0   0   0 |  1   4   1   0   0   2   2   0   0   0   0   0  0   0 |  2  2  0  1   4   1   0   0  0  0 | 1  2  2  0
.... .... ....    x... ....     & |   2   0 |   * 960   *   *   *   * |   0   1   2   1   0   0   1   0   0   0   0 |  0   2   1   1   2   0   1   0   2   1   0   0  0   0 |  1  2  1  0   2   1   1   2  0  0 | 1  1  2  1
oo..3oo..3oo.. *b3oo..3oo..&#x  & |   1   1 |   *   * 960   *   *   * |   0   0   0   0   1   2   2   0   0   0   0 |  0   0   0   0   0   2   2   1   4   1   0   0  0   0 |  0  0  0  1   4   1   2   2  0  0 | 0  2  2  1
.x.. .... ....    .... ....     & |   0   2 |   *   *   * 160   *   * |   0   0   0   0   3   0   0   0   0   2   0 |  0   0   0   0   0   6   3   0   0   0   0   0  1   0 |  0  0  0  3   6   1   0   0  0  0 | 0  3  2  0
.... .x.. ....    .... ....     & |   0   2 |   *   *   *   * 960   * |   0   0   0   0   0   1   0   1   2   0   1 |  0   0   0   0   0   2   0   1   2   0   2   1  0   2 |  0  0  0  1   4   0   2   1  1  1 | 0  2  2  1
.oo.3.oo.3.oo. *b3.oo.3.oo.&#x    |   0   2 |   *   *   *   *   * 320 |   0   0   0   0   0   0   0   0   0   2   3 |  0   0   0   0   0   6   0   0   0   0   0   0  1   3 |  0  0  0  3   6   0   0   0  0  1 | 0  3  2  0
----------------------------------+---------+-------------------------+---------------------------------------------+-------------------------------------------------------+-----------------------------------+-----------
x...3o... ....    .... ....     & |   3   0 |   3   0   0   0   0   0 | 320   *   *   *   *   *   *   *   *   *   * |  1   2   0   0   0   1   0   0   0   0   0   0  0   0 |  2  1  0  1   2   0   0   0  0  0 | 1  2  1  0
x... .... ....    x... ....     & |   4   0 |   2   2   0   0   0   0 |   * 480   *   *   *   *   *   *   *   *   * |  0   2   1   0   0   0   1   0   0   0   0   0  0   0 |  1  2  0  0   2   1   0   0  0  0 | 1  1  2  0
.... o... .... *b3x... ....     & |   3   0 |   0   3   0   0   0   0 |   *   * 640   *   *   *   *   *   *   *   * |  0   1   0   1   1   0   0   0   1   0   0   0  0   0 |  1  1  1  0   1   0   1   1  0  0 | 1  1  1  1
.... .... ....    x...3o...     & |   3   0 |   0   3   0   0   0   0 |   *   *   * 320   *   *   *   *   *   *   * |  0   0   1   0   2   0   0   0   0   1   0   0  0   0 |  0  2  1  0   0   1   0   2  0  0 | 1  0  2  1
xx.. .... ....    .... ....&#x  & |   2   2 |   1   0   2   1   0   0 |   *   *   *   * 480   *   *   *   *   *   * |  0   0   0   0   0   2   2   0   0   0   0   0  0   0 |  0  0  0  1   4   1   0   0  0  0 | 0  2  2  0
.... ox.. ....    .... ....&#x  & |   1   2 |   0   0   2   0   1   0 |   *   *   *   *   * 960   *   *   *   *   * |  0   0   0   0   0   1   0   1   2   0   0   0  0   0 |  0  0  0  1   2   0   2   1  0  0 | 0  2  1  1
.... .... ....    xo.. ....&#x  & |   2   1 |   0   1   2   0   0   0 |   *   *   *   *   *   * 960   *   *   *   * |  0   0   0   0   0   0   1   0   2   1   0   0  0   0 |  0  0  0  0   2   1   1   2  0  0 | 0  1  2  1
.... .x..3.o..    .... ....     & |   0   3 |   0   0   0   0   3   0 |   *   *   *   *   *   *   * 320   *   *   * |  0   0   0   0   0   1   0   1   0   0   2   0  0   0 |  0  0  0  1   2   0   2   0  1  0 | 0  2  1  1
.... .x.. .... *b3.o.. ....     & |   0   3 |   0   0   0   0   3   0 |   *   *   *   *   *   *   *   * 640   *   * |  0   0   0   0   0   0   0   0   1   0   1   1  0   1 |  0  0  0  0   2   0   1   1  1  1 | 0  1  2  1
.xo. .... ....    .... ....&#x  & |   0   3 |   0   0   0   1   0   2 |   *   *   *   *   *   *   *   *   * 320   * |  0   0   0   0   0   3   0   0   0   0   0   0  1   0 |  0  0  0  3   3   0   0   0  0  0 | 0  3  1  0
.... .xx. ....    .... ....&#x    |   0   4 |   0   0   0   0   2   2 |   *   *   *   *   *   *   *   *   *   * 480 |  0   0   0   0   0   2   0   0   0   0   0   0  0   2 |  0  0  0  1   4   0   0   0  0  1 | 0  2  2  0
----------------------------------+---------+-------------------------+---------------------------------------------+-------------------------------------------------------+-----------------------------------+-----------
x...3o...3o...    .... ....     & ♦   4   0 |   6   0   0   0   0   0 |   4   0   0   0   0   0   0   0   0   0   0 | 80   *   *   *   *   *   *   *   *   *   *   *  *   * |  2  0  0  1   0   0   0   0  0  0 | 1  2  0  0
x...3o... .... *b3x... ....     & ♦  12   0 |  12  12   0   0   0   0 |   4   6   4   0   0   0   0   0   0   0   0 |  * 160   *   *   *   *   *   *   *   *   *   *  *   * |  1  1  0  0   1   0   0   0  0  0 | 1  1  1  0
x... .... ....    x...3o...     & ♦   6   0 |   3   6   0   0   0   0 |   0   3   0   2   0   0   0   0   0   0   0 |  *   * 160   *   *   *   *   *   *   *   *   *  *   * |  0  2  0  0   0   1   0   0  0  0 | 1  0  2  0
.... o...3o... *b3x... ....     & ♦   4   0 |   0   6   0   0   0   0 |   0   0   4   0   0   0   0   0   0   0   0 |  *   *   * 160   *   *   *   *   *   *   *   *  *   * |  1  0  1  0   0   0   1   0  0  0 | 1  1  0  1
.... o... .... *b3x...3o...     & ♦   6   0 |   0  12   0   0   0   0 |   0   0   4   4   0   0   0   0   0   0   0 |  *   *   *   * 160   *   *   *   *   *   *   *  *   * |  0  1  1  0   0   0   0   1  0  0 | 1  0  1  1
xxo.3oxx. ....    .... ....&#xt & ♦   3   9 |   3   0   6   3   6   6 |   1   0   0   0   3   3   0   1   0   3   3 |  *   *   *   *   * 320   *   *   *   *   *   *  *   * |  0  0  0  1   2   0   0   0  0  0 | 0  2  1  0
xx.. .... ....    xo.. ....&#x  & ♦   4   2 |   2   2   4   1   0   0 |   0   1   0   0   2   0   2   0   0   0   0 |  *   *   *   *   *   * 480   *   *   *   *   *  *   * |  0  0  0  0   2   1   0   0  0  0 | 0  1  2  0
.... ox..3oo..    .... ....&#x  & ♦   1   3 |   0   0   3   0   3   0 |   0   0   0   0   0   3   0   1   0   0   0 |  *   *   *   *   *   *   * 320   *   *   *   *  *   * |  0  0  0  1   0   0   2   0  0  0 | 0  2  0  1
.... ox.. .... *b3xo.. ....&#x  & ♦   3   3 |   0   3   6   0   3   0 |   0   0   1   0   0   3   3   0   1   0   0 |  *   *   *   *   *   *   *   * 640   *   *   *  *   * |  0  0  0  0   1   0   1   1  0  0 | 0  1  1  1
.... .... ....    xo..3oo..&#x  & ♦   3   1 |   0   3   3   0   0   0 |   0   0   0   1   0   0   3   0   0   0   0 |  *   *   *   *   *   *   *   *   * 320   *   *  *   * |  0  0  0  0   0   1   0   2  0  0 | 0  0  2  1
.... .x..3.o.. *b3.o.. ....     & ♦   0   6 |   0   0   0   0  12   0 |   0   0   0   0   0   0   0   4   4   0   0 |  *   *   *   *   *   *   *   *   *   * 160   *  *   * |  0  0  0  0   1   0   1   0  1  0 | 0  1  1  1
.... .x.. .... *b3.o..3.o..     & ♦   0   4 |   0   0   0   0   6   0 |   0   0   0   0   0   0   0   0   4   0   0 |  *   *   *   *   *   *   *   *   *   *   * 160  *   * |  0  0  0  0   0   0   0   1  1  1 | 0  0  2  1
.xo. .... .ox.    .... ....&#x    ♦   0   4 |   0   0   0   2   0   4 |   0   0   0   0   0   0   0   0   0   4   0 |  *   *   *   *   *   *   *   *   *   *   *   * 80   * |  0  0  0  3   0   0   0   0  0  0 | 0  3  0  0
.... .xx. .... *b3.oo. ....&#x    ♦   0   6 |   0   0   0   0   6   3 |   0   0   0   0   0   0   0   0   2   0   3 |  *   *   *   *   *   *   *   *   *   *   *   *  * 320 |  0  0  0  0   2   0   0   0  0  1 | 0  1  2  0
----------------------------------+---------+-------------------------+---------------------------------------------+-------------------------------------------------------+-----------------------------------+-----------
x...3o...3o... *b3x... ....     & ♦  32   0 |  48  48   0   0   0   0 |  32  24  32   0   0   0   0   0   0   0   0 |  8   8   0   8   0   0   0   0   0   0   0   0  0   0 | 20  *  *  *   *   *   *   *  *  * | 1  1  0  0
x...3o... .... *b3x...3o...     & ♦  30   0 |  30  60   0   0   0   0 |  10  30  20  20   0   0   0   0   0   0   0 |  0   5  10   0   5   0   0   0   0   0   0   0  0   0 |  * 32  *  *   *   *   *   *  *  * | 1  0  1  0
.... o...3o... *b3x...3o...     & ♦  10   0 |   0  30   0   0   0   0 |   0   0  20  10   0   0   0   0   0   0   0 |  0   0   0   5   5   0   0   0   0   0   0   0  0   0 |  *  * 32  *   *   *   *   *  *  * | 1  0  0  1
xxoo3oxxo3ooxx    .... ....&#xt   ♦   8  24 |  12   0  24  12  24  24 |   8   0   0   0  12  24   0   8   0  24  12 |  2   0   0   0   0   8   0   8   0   0   0   0  6   0 |  *  *  * 40   *   *   *   *  *  * | 0  2  0  0
xxo.3oxx. .... *b3xoo. ....&#xt & ♦  12  18 |  12  12  24   6  24  12 |   4   6   4   0  12  12  12   4   8   6  12 |  0   1   0   0   0   4   6   0   4   0   1   0  0   4 |  *  *  *  * 160   *   *   *  *  * | 0  1  1  0
xx.. .... ....    xo..3oo..&#x  & ♦   6   2 |   3   6   6   1   0   0 |   0   3   0   2   3   0   6   0   0   0   0 |  0   0   1   0   0   0   3   0   0   2   0   0  0   0 |  *  *  *  *   * 160   *   *  *  * | 0  0  2  0
.... ox..3oo.. *b3xo.. ....&#x  & ♦   4   6 |   0   6  12   0  12   0 |   0   0   4   0   0  12   6   4   4   0   0 |  0   0   0   1   0   0   0   4   4   0   1   0  0   0 |  *  *  *  *   *   * 160   *  *  * | 0  1  0  1
.... ox.. .... *b3xo..3oo..&#x  & ♦   6   4 |   0  12  12   0   6   0 |   0   0   4   4   0   6  12   0   4   0   0 |  0   0   0   0   1   0   0   0   4   4   0   1  0   0 |  *  *  *  *   *   *   * 160  *  * | 0  0  1  1
.... .x..3.o.. *b3.o..3.o..     & ♦   0  10 |   0   0   0   0  30   0 |   0   0   0   0   0   0   0  10  20   0   0 |  0   0   0   0   0   0   0   0   0   0   5   5  0   0 |  *  *  *  *   *   *   *   * 32  * | 0  0  1  1
.... .xx. .... *b3.oo.3.oo.&#x    ♦   0   8 |   0   0   0   0  12   4 |   0   0   0   0   0   0   0   0   8   0   6 |  0   0   0   0   0   0   0   0   0   0   0   2  0   4 |  *  *  *  *   *   *   *   *  * 80 | 0  0  2  0
----------------------------------+---------+-------------------------+---------------------------------------------+-------------------------------------------------------+-----------------------------------+-----------
x...3o...3o... *b3x...3o...     & ♦ 160   0 | 240 480   0   0   0   0 | 160 240 320 160   0   0   0   0   0   0   0 | 40  80  80  80  80   0   0   0   0   0   0   0  0   0 | 10 16 16  0   0   0   0   0  0  0 | 2  *  *  *
xxoo3oxxo3ooxx *b3xoox ....&#xt   ♦  64  96 |  96  96 192  48 192  96 |  64  48  64   0  96 192  96  64  64  96  96 | 16  16   0  16   0  64  48  64  64   0  16   0 24  32 |  2  0  0  8  16   0  16   0  0  0 | * 10  *  *
xxo.3oxx. .... *b3xoo.3ooo.&#xt & ♦  30  30 |  30  60  60  10  60  20 |  10  30  20  20  30  30  60  10  40  10  30 |  0   5  10   0   5  10  30   0  20  20   5  10  0  20 |  0  1  0  0   5  10   0   5  1  5 | *  * 32  *
.... ox..3oo.. *b3xo..3oo..&#x  & ♦  10  10 |   0  30  30   0  30   0 |   0   0  20  10   0  30  30  10  20   0   0 |  0   0   0   5   5   0   0  10  20  10   5   5  0   0 |  0  0  1  0   0   0   5   5  1  0 | *  *  * 32

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