Acronym ...
Name tetrahedral - n-prismantiprismoid
Circumradius ...
Especially s4o2o3o4s (n=2: hin)   s6o2o3o4s (n=3)  
Confer
general polytopal classes:
isogonal  

These isogonal polytera are obtained by hemiation of 2n-cube duoprism. But because of lower degree of freedom the resulting edge sizes cannot be made all alike.

The exceptional case n=2 could be considered similarily, but the incidence matrices below will be different because of degeneracy. Then it becomes the hemiated pent (hin) and even happens to become uniform.


Incidence matrix according to Dynkin symbol

s2no2o3o4s   (n > 2)

demi( .  . . . . ) | 8n |   6   3  2 | 1   9  18  3 |  3   6  1  12   8 | 3  2  5
-------------------+----+------------+--------------+-------------------+--------
      s  . 2 . s   |  2 | 24n   *  * | 0   2   4  0 |  1   2  0   4   2 | 2  1  2  q
      .  . . o4s   |  2 |   * 12n  * | 0   0   4  2 |  0   2  1   2   4 | 1  2  2  q
sefa( s2no . . . ) |  2 |   *   * 8n | 1   3   0  0 |  3   0  0   3   0 | 3  0  1  y = x(2n)
-------------------+----+------------+--------------+-------------------+--------
      s2no . . .   |  n |   0   0  n | 8   *   *  * |  3   0  0   0   0 | 3  0  0  yno
sefa( s2no 2 . s ) |  3 |   2   0  1 | * 24n   *  * |  1   0  0   2   0 | 2  0  1  oy&#q
sefa( s  . 2 o4s ) |  3 |   2   1  0 | *   * 48n  * |  0   1  0   1   1 | 1  1  1  q3o
sefa( .  . o3o4s ) |  3 |   0   3  0 | *   *   * 8n |  0   0  1   0   2 | 0  2  1  q3o
-------------------+----+------------+--------------+-------------------+--------
      s2no 2 . s   | 2n |  2n   0 2n | 2  2n   0  0 | 12   *  *   *   * | 2  0  0  oy-n-yo&#q (n-ap variant)
      s  . 2 o4s   |  4 |   4   2  0 | 0   0   4  0 |  * 12n  *   *   * | 1  1  0  q-tet
      .  . o3o4s   |  4 |   0   6  0 | 0   0   0  4 |  *   * 2n   *   * | 0  2  0  q-tet
sefa( s2no 2 o4s ) |  4 |   4   1  1 | 0   2   2  0 |  *   *  * 24n   * | 1  0  1  yo2oq&#q (disphenoid, tet variant)
sefa( s  2 o3o4s ) |  4 |   3   3  0 | 0   0   3  1 |  *   *  *   * 16n | 0  1  1  q-tet
-------------------+----+------------+--------------+-------------------+--------
      s2no 2 o4s   | 4n |  8n  1n 4n | 4  8n  8n  0 |  4  2n  0  4n   0 | 6  *  *  2,n-dap
      s  2 o3o4s   |  8 |  12  12  0 | 0   0  24  8 |  0   6  2   0   8 | * 2n  *  q-hex
sefa( s2no2o3o4s ) |  5 |   6   3  1 | 0   3   6  1 |  0   0  0   3   2 | *  * 8n  yo2oq3oo&#q (tepe variant)

starting figure: x2no o3o4x

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