Acronym ...
Name tetrahedral - 2n-prismantiprismoid
Circumradius ...
Especially s4x2o3o4s (n=2)   s6x2o3o4s (n=3)  
Confer
general polytopal classes:
isogonal  

These isogonal polytera are obtained by hemiation of 4n-cube duoprism. But because of lower degree of freedom the resulting edge sizes cannot be made all alike.


Incidence matrix according to Dynkin symbol

s2nx2o3o4s   (n > 1)

demi( .  . . . . ) | 16n |  1   3   3  1 | 1   3   6   9   3 |  3   3  1   9   4  3 | 3  1  1  4
-------------------+-----+---------------+-------------------+----------------------+-----------
demi( .  x . . . ) |   2 | 8n   *   *  * | 1   3   3   0   0 |  3   0   0   6  0  3 | 3  0  1  3  x
      s  . 2 . s   |   2 |  * 24n   *  * | 0   0   2   4   0 |  1   2  0   4   2  0 | 2  1  0  2  q
      .  . . o4s   |   2 |  *   * 24n  * | 0   1   0   2   2 |  0   1  1   2   2  2 | 1  1  1  2  q
sefa( s2nx . . . ) |   2 |  *   *   * 8n | 1   0   3   0   0 |  3   0  0   3   0  0 | 3  0  0  1  y = x(4n,3)
-------------------+-----+---------------+-------------------+----------------------+-----------
      s2nx . . .   |  2n |  n   0   0  n | 8   *   *   *   * |  3   0  0   0   0  0 | 3  0  0  0  xny
      .  x 2 o4s   |   4 |  2   0   2  0 | * 12n   *   *   * |  0   0  0   2   0  2 | 1  0  1  2  x2q
sefa( s2nx 2 . s ) |   4 |  1   2   0  1 | *   * 24n   *   * |  1   0  0   2   0  0 | 2  0  0  1  xy&#q
sefa( s  . 2 o4s ) |   3 |  0   2   1  0 | *   *   * 48n   * |  0   1  0   1   1  0 | 1  1  0  1  q3o
sefa( .  . o3o4s ) |   3 |  0   0   3  0 | *   *   *   * 16n |  0   0  1   0   1  1 | 0  1  1  1  q3o
-------------------+-----+---------------+-------------------+----------------------+-----------
      s2nx 2 . s   |  4n | 2n  2n   0 2n | 2   0  2n   0   0 | 12   *  *   *   *  * | 2  0  0  0  xy-2n-yx&#q (di-n-gonal trapezoprism)
      s  . 2 o4s   |   4 |  0   4   2  0 | 0   0   0   4   0 |  * 12n  *   *   *  * | 1  1  0  0  q-tet
      .  . o3o4s   |   4 |  0   0   6  0 | 0   0   0   0   4 |  *   * 4n   *   *  * | 0  1  1  0  q-tet
sefa( s2nx 2 o4s ) |   6 |  2   4   2  1 | 0   1   2   2   0 |  *   *  * 24n   *  * | 1  0  0  1  yx2oq&#q (wedge-like trip variant)
sefa( s  2 o3o4s ) |   4 |  0   3   3  0 | 0   0   0   3   1 |  *   *  *   * 16n  * | 0  1  0  1  q-tet
sefa( .  x2o3o4s ) |   6 |  3   0   6  0 | 0   3   0   0   2 |  *   *  *   *   * 8n | 0  0  1  1  x q3o (trip variant)
-------------------+-----+---------------+-------------------+----------------------+-----------
      s2nx 2 o4s   |  8n | 4n  8n  4n 4n | 4  2n  8n  8n   0 |  4  2n  0  4n   0  0 | 6  *  *  *  2-2n prismantiprismoid
      s  2 o3o4s   |   8 |  0  12  12  0 | 0   0   0  24   8 |  0   6  2   0   8  0 | * 2n  *  *  q-hex
      .  x2o3o4s   |   8 |  4   0  12  0 | 0   6   0   0   8 |  0   0  2   0   0  4 | *  * 2n  *  x q3o3o (tepe variant)
sefa( s2nx2o3o4s ) |   8 |  3   6   6  1 | 0   3   3   6   2 |  0   0  0   3   2  1 | *  *  * 8n  yx2oq3oo&#q (tepe variant)

starting figure: x2nx o3o4x

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