Acronym	prissia
Name	prismatorhombisnub icositetrachoric alterprism, triangle-alternation of prismatorhombated icositetrachoric prism
Circumradius	sqrt[33+12 sqrt(2)]/2 = 3.534493
Face vector	576, 2880, 4224, 2256, 338
Confer	general polytopal classes: isogonal
External links

This isogonal polyteron is obtained by a hemiation of pricope wrt. its triangles. But because of lower degree of freedom the resulting edge sizes cannot be made all alike.

Incidence matrix according to Dynkin symbol

s2s3s4o3x

demi( . . . . . ) | 576 |   2   1   2   1    4 |   1   2   2   2    6   3   3   4   2 |   2  1   1  1   2  1   4   6   3   3 |  1  2  1 1   4
------------------+-----+----------------------+--------------------------------------+--------------------------------------+---------------
demi( . . . . x ) |   2 | 576   *   *   *    * |   1   0   1   1    0   0   0   2   1 |   0  1   0  0   1  1   0   3   2   2 |  0  1  1 1   3
      s2s . . .   |   2 |   * 288   *   *    * |   0   0   2   0    4   0   0   0   0 |   2  1   0  0   0  0   2   4   0   0 |  1  2  0 0   2  q
      s 2 s . .   |   2 |   *   * 576   *    * |   0   0   0   1    2   2   0   0   0 |   1  0   1  0   0  0   2   2   2   0 |  1  1  1 0   2  q
      . . s4o .   |   2 |   *   *   * 288    * |   0   0   0   0    0   2   2   0   2 |   0  0   1  1   0  1   2   0   2   2 |  1  0  1 1   2  q
sefa( . s3s . . ) |   2 |   *   *   *   * 1152 |   0   1   0   0    1   0   1   1   0 |   1  0   0  1   1  0   1   1   0   1 |  1  1  0 1   1  h
------------------+-----+----------------------+--------------------------------------+--------------------------------------+---------------
demi( . . . o3x ) |   3 |   3   0   0   0    0 | 192   *   *   *    *   *   *   *   * |   0  1   0  0   0  1   0   0   1   1 |  0  0  1 1   2
      . s3s . .   |   3 |   0   0   0   0    3 |   * 384   *   *    *   *   *   *   * |   1  0   0  1   1  0   0   0   0   0 |  1  1  0 1   0  h3o
      s2s . 2 x   |   4 |   2   2   0   0    0 |   *   * 288   *    *   *   *   *   * |   0  1   0  0   0  0   0   2   0   0 |  0  1  0 0   2  x2q
      s 2 s 2 x   |   4 |   2   0   2   0    0 |   *   *   * 288    *   *   *   *   * |   0  0   0  0   0  0   0   2   2   0 |  0  1  1 0   2  x2q
sefa( s2s3s . . ) |   3 |   0   1   1   0    1 |   *   *   *   * 1152   *   *   *   * |   1  0   0  0   0  0   1   1   0   0 |  1  1  0 0   1  oh&#q
sefa( s 2 s4o . ) |   3 |   0   0   2   1    0 |   *   *   *   *    * 576   *   *   * |   0  0   1  0   0  0   1   0   1   0 |  1  0  1 0   1  q3o
sefa( . s3s4o . ) |   3 |   0   0   0   1    2 |   *   *   *   *    *   * 576   *   * |   0  0   0  1   0  0   1   0   0   1 |  1  0  0 1   1  oq&#h
sefa( . s3s 2 x ) |   4 |   2   0   0   0    2 |   *   *   *   *    *   *   * 576   * |   0  0   0  0   1  0   0   1   0   1 |  0  1  0 1   1  x2h
sefa( . . s4o3x ) |   6 |   3   0   0   3    0 |   *   *   *   *    *   *   *   * 192 |   0  0   0  0   0  1   0   0   1   1 |  0  0  1 1   1  x3q
------------------+-----+----------------------+--------------------------------------+--------------------------------------+---------------
      s2s3s . .   |   6 |   0   3   3   0    6 |   0   2   0   0    6   0   0   0   0 | 192  *   *  *   *  *   *   *   *   * |  1  1  0 0   0  ho3oh&#q
      s2s 2 o3x   |   6 |   6   3   0   0    0 |   2   0   3   0    0   0   0   0   0 |   * 96   *  *   *  *   *   *   *   * |  0  0  0 0   2  q x3o
      s 2 s4o .   |   4 |   0   0   4   2    0 |   0   0   0   0    0   4   0   0   0 |   *  * 144  *   *  *   *   *   *   * |  1  0  1 0   0  q3o3o
      . s3s4o .   |  12 |   0   0   0   6   24 |   0   8   0   0    0   0  12   0   0 |   *  *   * 48   *  *   *   *   *   * |  1  0  0 1   0  qQo oqQ Qoq&#zh
      . s3s 2 x   |   6 |   3   0   0   0    6 |   0   2   0   0    0   0   0   3   0 |   *  *   *  * 192  *   *   *   *   * |  0  1  0 1   0  x h3o
      . . s4o3x   |  12 |  12   0   0   6    0 |   4   0   0   0    0   0   0   0   4 |   *  *   *  *   * 48   *   *   *   * |  0  0  1 1   0  q3x3o
sefa( s2s3s4o . ) |   4 |   0   1   2   1    2 |   0   0   0   0    2   1   1   0   0 |   *  *   *  *   *  * 576   *   *   * |  1  0  0 0   1  q-laced oq&#h pyramid (tet variant)
sefa( s2s3s 2 x ) |   6 |   3   2   2   0    2 |   0   0   1   1    2   0   0   1   0 |   *  *   *  *   *  *   * 576   *   * |  0  1  0 0   1  xx oh&#q (trip variant)
sefa( s 2 s4o3x ) |   9 |   6   0   6   3    0 |   1   0   0   3    0   3   0   0   1 |   *  *   *  *   *  *   *   * 192   * |  0  0  1 0   1  xx3oq&#q (tricu variant)
sefa( . s3s4o3x ) |   9 |   6   0   0   3    6 |   1   0   0   0    0   0   3   3   1 |   *  *   *  *   *  *   *   *   * 192 |  0  0  0 1   1  xx3oq&#h (tricu variant)
------------------+-----+----------------------+--------------------------------------+--------------------------------------+---------------
      s2s3s4o .   |  24 |   0  12  24  12   48 |   0  16   0   0   48  24  24   0   0 |   8  0   6  2   0  0  24   0   0   0 | 24  *  * *   *  pikap
      s2s3s 2 x   |  12 |   6   6   6   0   12 |   0   4   3   3   12   0   0   6   0 |   2  0   0  0   2  0   0   6   0   0 |  * 96  * *   *  xx ho3oh&#q (ope variant)
      s 2 s4o3x   |  24 |  24   0  24  12    0 |   8   0   0  12    0  24   0   0   8 |   0  0   6  0   0  2   0   0   8   0 |  *  * 24 *   *  qo3xx3oq&#q (tuta variant)
      . s3s4o3x   | 288 | 288   0   0 144  576 |  96 192   0   0    0   0 288 288  96 |   0  0   0 24  96 24   0   0   0  96 |  *  *  * 2   *  qoQ3xxx3Qqo *b3oQq&#zh
sefa( s2s3s4o3x ) |  12 |   9   3   6   3    6 |   2   0   3   3    6   3   3   3   1 |   0  1   0  0   0  0   3   3   1   1 |  *  *  * * 192  xxx3ooq&#(q,q,h) (tricuf variant)

starting figure: x2x3x4o3x