This generally isogonal polychoron happens to become prissi for a=d=e=x and c=f.

The case d=0 would belong here as limiting case too, although some elements then become degenerate and so it has slightly different incidences, as shown separately in aoc3ooo3cao *b3oca&#ze.

Incidence matrix according to Dynkin symbol

aoc3ddd3cao *b3oca&#ze   → height = 0
                           0 < a < c
                           d > 0
                           e = sqrt[(a2-ac+c2)/2]

o..3o..3o.. *b3o..     & | 288 |   1   2   4 |  2  1   3   4   2 |  1  3  2  1
-------------------------+-----+-------------+-------------------+------------
a.. ... ...    ...     & |   2 | 144   *   * |  2  0   2   0   0 |  1  2  0  1  a
... d.. ...    ...     & |   2 |   * 288   * |  1  1   0   2   0 |  1  2  1  0  d
oo.3oo.3oo. *b3oo.&#e  & |   2 |   *   * 576 |  0  0   1   1   1 |  0  1  1  1  e
-------------------------+-----+-------------+-------------------+------------
a..3d.. ...    ...     & |   6 |   3   3   0 | 96  *   *   *   * |  1  1  0  0
... d.. ... *b3o..     & |   3 |   0   3   0 |  * 96   *   *   * |  1  1  0  0
ao. ... ...    ...&#e  & |   3 |   1   0   2 |  *  * 288   *   * |  0  1  0  1
... dd. ...    ...&#e  & |   4 |   0   2   2 |  *  *   * 288   * |  0  1  1  0
ooo3ooo3ooo *b3ooo&#e    |   3 |   0   0   3 |  *  *   *   * 192 |  0  0  1  1
-------------------------+-----+-------------+-------------------+------------
a..3d.. ... *b3o..     & |  12 |   6  12   0 |  4  4   0   0   0 | 24  *  *  *  (a,d)-tut
ao.3dd. ...    ...&#e  & |   9 |   3   6   6 |  1  1   3   3   0 |  * 96  *  *  (a,d,e)-tricu
... ddd ...    ...&#e    |   6 |   0   3   6 |  0  0   0   3   2 |  *  * 96  *  (d,e)-trip
aoc ... coa    oca&#ze   |  12 |   6   0  24 |  0  0  12   0   8 |  *  *  * 24  pyritohedral (a,c,e)-ike