Acronym	...
Name	tetrahedral - square-prismantiprismoid
Circumradius	...
Face vector	32, 128, 208, 140, 30
Confer	more general: s2nx2o3o4s   general polytopal classes: isogonal
External links

This isogonal polyteron is obtained by hemiation of ocube. But because of lower degree of freedom the resulting edge sizes cannot be made all alike.

Incidence matrix according to Dynkin symbol

s4x2o3o4s

demi( . . . . . ) | 32 |  1  3  3  1 | 1  3  6  9  3 |  3  3 1  9  4  3 | 3 1 1  4
------------------+----+-------------+---------------+------------------+---------
demi( . x . . . ) |  2 | 16  *  *  * | 1  3  3  0  0 |  3  0 0  6  0  3 | 3 0 1  3  x
      s . 2 . s   |  2 |  * 48  *  * | 0  0  2  4  0 |  1  2 0  4  2  0 | 2 1 0  2  q
      . . . o4s   |  2 |  *  * 48  * | 0  1  0  2  2 |  0  1 1  2  2  2 | 1 1 1  2  q
sefa( s4x . . . ) |  2 |  *  *  * 16 | 1  0  3  0  0 |  3  0 0  3  0  0 | 3 0 0  1  w
------------------+----+-------------+---------------+------------------+---------
      s4x . . .   |  4 |  2  0  0  2 | 8  *  *  *  * |  3  0 0  0  0  0 | 3 0 0  0  x2w
      . x 2 o4s   |  4 |  2  0  2  0 | * 24  *  *  * |  0  0 0  2  0  2 | 1 0 1  2  x2q
sefa( s4x 2 . s ) |  4 |  1  2  0  1 | *  * 48  *  * |  1  0 0  2  0  0 | 2 0 0  1  xw&#q
sefa( s . 2 o4s ) |  3 |  0  2  1  0 | *  *  * 96  * |  0  1 0  1  1  0 | 1 1 0  1  q3o
sefa( . . o3o4s ) |  3 |  0  0  3  0 | *  *  *  * 32 |  0  0 1  0  1  1 | 0 1 1  1  q3o
------------------+----+-------------+---------------+------------------+---------
      s4x 2 . s   |  8 |  4  4  0  4 | 2  0  4  0  0 | 12  * *  *  *  * | 2 0 0  0  xw2wx&#q (recta)
      s . 2 o4s   |  4 |  0  4  2  0 | 0  0  0  4  0 |  * 24 *  *  *  * | 1 1 0  0  q-tet
      . . o3o4s   |  4 |  0  0  6  0 | 0  0  0  0  4 |  *  * 8  *  *  * | 0 1 1  0  q-tet
sefa( s4x 2 o4s ) |  6 |  2  4  2  1 | 0  1  2  2  0 |  *  * * 48  *  * | 1 0 0  1  wx2oq&#q (wedge-like trip variant)
sefa( s 2 o3o4s ) |  4 |  0  3  3  0 | 0  0  0  3  1 |  *  * *  * 32  * | 0 1 0  1  q-tet
sefa( . x2o3o4s ) |  6 |  3  0  6  0 | 0  3  0  0  2 |  *  * *  *  * 16 | 0 0 1  1  x q3o (trip variant)
------------------+----+-------------+---------------+------------------+---------
      s4x 2 o4s   | 16 |  8 16  8  8 | 4  4 16 16  0 |  4  4 0  8  0  0 | 6 * *  *  square prismantiprismoid
      s 2 o3o4s   |  8 |  0 12 12  0 | 0  0  0 24  8 |  0  6 2  0  8  0 | * 4 *  *  q-hex
      . x2o3o4s   |  8 |  4  0 12  0 | 0  6  0  0  8 |  0  0 2  0  0  4 | * * 4  *  x q3o3o (tepe variant)
sefa( s4x2o3o4s ) |  8 |  3  6  6  1 | 0  3  3  6  2 |  0  0 0  3  2  1 | * * * 16  wx2oq3oo&#q (tepe variant)

starting figure: x4x o3o4x