Acronym ...
Name gadathiphi+600 2tet (?)
Circumradius sqrt[3-sqrt(5)] = 0.874032
General of army hi
Colonel of regiment gadtaxady
Confer gadtef pixady   gadathiphi  

As abstract polytope gadathiphi+600 2tet is isomorphic to sirdtapady+600 2tet, thereby replacing pentagrams by pentagons, resp. gissid by doe and qrid by srid.

This Grünbaumian fissary polychoron can be seen as gadathiphi, filling up the spaces of the 600 pseudo tet by duoble-covers thereof, cross-linking the boundaries, thus that it becomes a true dyadic polychoron again. Sure, the triangles coincide by pairs. And the larger class of edges likewise coincide pairwise. Moreover vertices are given with trigonal axial vertex figures, coinciding by 4 so that the compound of those vertex figures gets that ditetrahedral symmetry of the one its colonel.


Incidence matrix

x5/2o3/2x3o3*b

.   .   . .    | 2400 |    3    6 |    3    6    3    3 |   3   1    3   1
---------------+------+-----------+---------------------+-----------------
x   .   . .    |    2 | 3600    * |    2    2    0    0 |   2   1    1   0
.   .   x .    |    2 |    * 7200 |    0    1    1    1 |   1   0    1   1
---------------+------+-----------+---------------------+-----------------
x5/2o   . .    |    5 |    5    0 | 1440    *    *    * |   1   1    0   0
x   .   x .    |    4 |    2    2 |    * 3600    *    * |   1   0    1   0
.   o3/2x .    |    3 |    0    3 |    *    * 2400    * |   1   0    0   1
.   .   x3o    |    3 |    0    3 |    *    *    * 2400 |   0   0    1   1
---------------+------+-----------+---------------------+-----------------
x5/2o3/2x .       60 |   60   60 |   12   30   20    0 | 120   *    *   *
x5/2o   . o3*b    20 |   30    0 |   12    0    0    0 |   * 120    *   *
x   .   x3o        6 |    3    6 |    0    3    0    2 |   *   * 1200   *
.   o3/2x3o3*b     4 |    0   12 |    0    0    4    4 |   *   *    * 600

x5/2o3/2x3/2o3/2*b

.   .   .   .      | 2400 |    3    6 |    3    6    3    3 |   3   1    3   1
-------------------+------+-----------+---------------------+-----------------
x   .   .   .      |    2 | 3600    * |    2    2    0    0 |   2   1    1   0
.   .   x   .      |    2 |    * 7200 |    0    1    1    1 |   1   0    1   1
-------------------+------+-----------+---------------------+-----------------
x5/2o   .   .      |    5 |    5    0 | 1440    *    *    * |   1   1    0   0
x   .   x   .      |    4 |    2    2 |    * 3600    *    * |   1   0    1   0
.   o3/2x   .      |    3 |    0    3 |    *    * 2400    * |   1   0    0   1
.   .   x3/2o      |    3 |    0    3 |    *    *    * 2400 |   0   0    1   1
-------------------+------+-----------+---------------------+-----------------
x5/2o3/2x   .         60 |   60   60 |   12   30   20    0 | 120   *    *   *
x5/2o   .   o3/2*b    20 |   30    0 |   12    0    0    0 |   * 120    *   *
x   .   x3/2o          6 |    3    6 |    0    3    0    2 |   *   * 1200   *
.   o3/2x3/2o3/2*b     4 |    0   12 |    0    0    4    4 |   *   *    * 600

x5/3o3x3/2o3*b

.   . .   .    | 2400 |    3    6 |    3    6    3    3 |   3   1    3   1
---------------+------+-----------+---------------------+-----------------
x   . .   .    |    2 | 3600    * |    2    2    0    0 |   2   1    1   0
.   . x   .    |    2 |    * 7200 |    0    1    1    1 |   1   0    1   1
---------------+------+-----------+---------------------+-----------------
x5/3o .   .    |    5 |    5    0 | 1440    *    *    * |   1   1    0   0
x   . x   .    |    4 |    2    2 |    * 3600    *    * |   1   0    1   0
.   o3x   .    |    3 |    0    3 |    *    * 2400    * |   1   0    0   1
.   . x3/2o    |    3 |    0    3 |    *    *    * 2400 |   0   0    1   1
---------------+------+-----------+---------------------+-----------------
x5/3o3x   .       60 |   60   60 |   12   30   20    0 | 120   *    *   *
x5/3o .   o3*b    20 |   30    0 |   12    0    0    0 |   * 120    *   *
x   . x3/2o        6 |    3    6 |    0    3    0    2 |   *   * 1200   *
.   o3x3/2o3*b     4 |    0   12 |    0    0    4    4 |   *   *    * 600

x5/3o3x3o3/2*b

.   . . .      | 2400 |    3    6 |    3    6    3    3 |   3   1    3   1
---------------+------+-----------+---------------------+-----------------
x   . . .      |    2 | 3600    * |    2    2    0    0 |   2   1    1   0
.   . x .      |    2 |    * 7200 |    0    1    1    1 |   1   0    1   1
---------------+------+-----------+---------------------+-----------------
x5/3o . .      |    5 |    5    0 | 1440    *    *    * |   1   1    0   0
x   . x .      |    4 |    2    2 |    * 3600    *    * |   1   0    1   0
.   o3x .      |    3 |    0    3 |    *    * 2400    * |   1   0    0   1
.   . x3o      |    3 |    0    3 |    *    *    * 2400 |   0   0    1   1
---------------+------+-----------+---------------------+-----------------
x5/3o3x .         60 |   60   60 |   12   30   20    0 | 120   *    *   *
x5/3o . o3/2*b    20 |   30    0 |   12    0    0    0 |   * 120    *   *
x   . x3o          6 |    3    6 |    0    3    0    2 |   *   * 1200   *
.   o3x3o3/2*b     4 |    0   12 |    0    0    4    4 |   *   *    * 600

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