Acronym sophax
Name small prismated hemihexeract,
runcinated demihexeract,
steric hexeract
Circumradius sqrt(11)/2 = 1.658312
Lace city
in approx. ASCII-art 
 ©  

h R r H		-- x3o3o *b3o3x (siphin)
R t T r		-- x3o3o *b3x3o (sirhin)
r T t R		-- o3o3x *b3x3o (alt. sirhin)
H r R h		-- o3o3x *b3o3x (alt. siphin)

where:
h = x3o3o *b3o (hex)
H = o3o3x *b3o (gyro hex)
r = o3o3x *b3x (rit)
R = x3o3o *b3x (gyro rit)
t = x3x3o *b3o (thex)
T = o3x3x *b3o (gyro thex)
Face vector 480, 3360, 7360, 6240, 1996, 236
Confer
related segmentopeta:
sirhina  
general polytopal classes:
Wythoffian polypeta   lace simplices  
External
links 		wikipedia   polytopewiki  

Incidence matrix according to Dynkin symbol

x3o3o *b3o3x3o

. . .    . . . | 480 |    6    8 |   12   24   12   4 |   4   4   24  12  12   8   6 |  1   8   8  12   6   2   4 |  2   4  4  1
---------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
x . .    . . . |   2 | 1440    * |    4    4    0   0 |   2   2    8   2   2   0   0 |  1   4   4   4   1   0   0 |  2   2  2  0
. . .    . x . |   2 |    * 1920 |    0    3    3   1 |   0   0    3   3   3   3   3 |  0   1   3   3   3   1   3 |  1   1  3  1
---------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
x3o .    . . . |   3 |    3    0 | 1920    *    *   * |   1   1    2   0   0   0   0 |  1   2   2   1   0   0   0 |  2   1  1  0
x . .    . x . |   4 |    2    2 |    * 2880    *   * |   0   0    2   1   1   0   0 |  0   1   2   2   1   0   0 |  1   1  2  0
. . .    o3x . |   3 |    0    3 |    *    * 1920   * |   0   0    0   1   0   2   1 |  0   0   2   0   1   1   2 |  1   0  2  1
. . .    . x3o |   3 |    0    3 |    *    *    * 640 |   0   0    0   0   3   0   3 |  0   0   0   3   3   0   3 |  0   1  3  1
---------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
x3o3o    . . . ♦   4 |    6    0 |    4    0    0   0 | 480   *    *   *   *   *   * |  1   2   0   0   0   0   0 |  2   1  0  0
x3o . *b3o . . ♦   4 |    6    0 |    4    0    0   0 |   * 480    *   *   *   *   * |  1   0   2   0   0   0   0 |  2   0  1  0
x3o .    . x . ♦   6 |    6    3 |    2    3    0   0 |   *   * 1920   *   *   *   * |  0   1   1   1   0   0   0 |  1   1  1  0
x . .    o3x . ♦   6 |    3    6 |    0    3    2   0 |   *   *    * 960   *   *   * |  0   0   2   0   1   0   0 |  1   0  2  0
x . .    . x3o ♦   6 |    3    6 |    0    3    0   2 |   *   *    *   * 960   *   * |  0   0   0   2   1   0   0 |  0   1  2  0
. o . *b3o3x . ♦   4 |    0    6 |    0    0    4   0 |   *   *    *   *   * 960   * |  0   0   1   0   0   1   1 |  1   0  1  1
. . .    o3x3o ♦   6 |    0   12 |    0    0    4   4 |   *   *    *   *   *   * 480 |  0   0   0   0   1   0   2 |  0   0  2  1
---------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
x3o3o *b3o . . ♦   8 |   24    0 |   32    0    0   0 |   8   8    0   0   0   0   0 | 60   *   *   *   *   *   * |  2   0  0  0
x3o3o    . x . ♦   8 |   12    4 |    8    6    0   0 |   2   0    4   0   0   0   0 |  * 480   *   *   *   *   * |  1   1  0  0
x3o . *b3o3x . ♦  20 |   30   30 |   20   30   20   0 |   0   5   10  10   0   5   0 |  *   * 192   *   *   *   * |  1   0  1  0
x3o .    . x3o ♦   9 |    9    9 |    3    9    0   3 |   0   0    3   0   3   0   0 |  *   *   * 640   *   *   * |  0   1  1  0
x . .    o3x3o ♦  12 |    6   24 |    0   12    8   8 |   0   0    0   4   4   0   2 |  *   *   *   * 240   *   * |  0   0  2  0
. o3o *b3o3x . ♦   5 |    0   10 |    0    0   10   0 |   0   0    0   0   0   5   0 |  *   *   *   *   * 192   * |  1   0  0  1
. o . *b3o3x3o ♦  10 |    0   30 |    0    0   20  10 |   0   0    0   0   0   5   5 |  *   *   *   *   *   * 192 |  0   0  1  1
---------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
x3o3o *b3o3x . ♦  80 |  240  160 |  320  240  160   0 |  80  80  160  80   0  80   0 | 10  40  16   0   0  16   0 | 12   *  *  *
x3o3o    . x3o ♦  12 |   18   12 |   12   18    0   4 |   3   0   12   0   6   0   0 |  0   3   0   4   0   0   0 |  * 160  *  *
x3o . *b3o3x3o ♦  60 |   90  180 |   60  180  120  60 |   0  15   60  60  60  30  30 |  0   0   6  20  15   0   6 |  *   * 32  *
. o3o *b3o3x3o ♦  15 |    0   60 |    0    0   60  20 |   0   0    0   0   0  30  15 |  0   0   0   0   0   6   6 |  *   *  * 32


o3x3o3o3o4s

demi( . . . . . . ) | 480 |    8    6 |   4   12   24   12 |   6   8  12  12   4   24   4 |   4   2   6   8  1  12   8 |  1   4  2  4
--------------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
demi( . x . . . . ) |   2 | 1920    * |   1    3    3    0 |   3   3   3   3   0    3   0 |   3   1   3   1  0   3   3 |  1   1  1  3
      . . . . o4s   |   2 |    * 1440 |   0    0    4    4 |   0   0   2   2   2    8   2 |   0   0   1   4  1   4   4 |  0   2  2  2
--------------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
demi( o3x . . . . ) |   3 |    3    0 | 640    *    *    * |   3   0   3   0   0    0   0 |   3   0   3   0  0   3   0 |  1   1  0  3
demi( . x3o . . . ) |   3 |    3    0 |   * 1920    *    * |   1   2   0   1   0    0   0 |   2   1   1   0  0   0   2 |  1   0  1  2
      . x . 2 o4s   |   4 |    2    2 |   *    * 2880    * |   0   0   1   1   0    2   0 |   0   0   1   1  0   2   2 |  0   1  1  2
sefa( . . . o3o4s ) |   3 |    0    3 |   *    *    * 1920 |   0   0   0   0   1    2   1 |   0   0   0   2  1   1   2 |  0   1  2  1
--------------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
demi( o3x3o . . . ) ♦   6 |   12    0 |   4    4    0    0 | 480   *   *   *   *    *   * |   2   0   1   0  0   0   0 |  1   0  0  2
demi( . x3o3o . . ) ♦   4 |    6    0 |   0    4    0    0 |   * 960   *   *   *    *   * |   1   1   0   0  0   0   1 |  1   0  1  1
      o3x . 2 o4s   ♦   6 |    6    3 |   2    0    3    0 |   *   * 960   *   *    *   * |   0   0   1   0  0   2   0 |  0   1  0  2
      . x3o 2 o4s   ♦   6 |    6    3 |   0    2    3    0 |   *   *   * 960   *    *   * |   0   0   1   0  0   0   2 |  0   0  1  2
      . . . o3o4s   ♦   4 |    0    6 |   0    0    0    4 |   *   *   *   * 480    *   * |   0   0   0   2  1   0   0 |  0   1  2  0
sefa( . x 2 o3o4s ) ♦   6 |    3    6 |   0    0    3    2 |   *   *   *   *   * 1920   * |   0   0   0   1  0   1   1 |  0   1  1  1
sefa( . . o3o3o4s ) ♦   4 |    0    6 |   0    0    0    4 |   *   *   *   *   *    * 480 |   0   0   0   0  1   0   2 |  0   0  2  1
--------------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
demi( o3x3o3o . . ) ♦  10 |   30    0 |  10   20    0    0 |   5   5   0   0   0    0   0 | 192   *   *   *  *   *   * |  1   0  0  1
demi( . x3o3o3o . ) ♦   5 |   10    0 |   0   10    0    0 |   0   5   0   0   0    0   0 |   * 192   *   *  *   *   * |  1   0  1  0
      o3x3o 2 o4s   ♦  12 |   24    6 |   8    8   12    0 |   2   0   4   4   0    0   0 |   *   * 240   *  *   *   * |  0   0  0  2
      . x 2 o3o4s   ♦   8 |    4   12 |   0    0    6    8 |   0   0   0   0   2    4   0 |   *   *   * 480  *   *   * |  0   1  1  0
      . . o3o3o4s   ♦   8 |    0   24 |   0    0    0   32 |   0   0   0   0   8    0   8 |   *   *   *   * 60   *   * |  0   0  2  0
sefa( o3x 2 o3o4s ) ♦   9 |    9    9 |   3    0    9    3 |   0   0   3   0   0    3   0 |   *   *   *   *  * 640   * |  0   1  0  1
sefa( . x3o3o3o4s ) ♦  20 |   30   30 |   0   20   30   20 |   0   5   0  10   0   10   5 |   *   *   *   *  *   * 192 |  0   0  1  1
--------------------+-----+-----------+--------------------+------------------------------+----------------------------+-------------
demi( o3x3o3o3o . ) ♦  15 |   60    0 |  20   60    0    0 |  15  30   0   0   0    0   0 |   6   6   0   0  0   0   0 | 32   *  *  *
      o3x 2 o3o4s   ♦  12 |   12   18 |   4    0   18   12 |   0   0   6   0   3   12   0 |   0   0   0   3  0   4   0 |  * 160  *  *
      . x3o3o3o4s   ♦  80 |  160  240 |   0  160  240  320 |   0  80   0  80  80  160  80 |   0  16   0  40 10   0  16 |  *   * 12  *
sefa( o3x3o3o3o4s ) ♦  60 |  180   90 |  60  120  180   60 |  30  30  60  60   0   60  15 |   6   0  15   0  0  20   6 |  *   *  * 32

starting figure: o3x3o3o3o4x


xxoo3oooo3ooxx *b3oxxo3xoox&#xt   → all heights = 1/sqrt(2) = 0.707107
(siphin || pseudo sirhin || pseudo alt sirhin || alt siphin)

...

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