As abstract polychoron geedatepthi is isomorphic to seedatepthi, thereby interchanging pentagons and pentagrams, resp. replacing gissid by doe, and stip by pip.

This Grünbaumian polychoron happens to have axial vertex figures, in fact vf3/2ov&#q, which coincide by 4 in a tetrahedral way. Thereby edges too can be seen to coincide by 3. Then geedatepthi belongs to the dattady regiment. As further the 2 classes of pentagrams happens to coincide one by one, this polychoron moreover is exotic.

Further it could be obtained as blend of dattathi with gidard tipady, blending out the doe. – Alternatively it could be obtained as blend of dittadphi with dard tipady, blending out the pip.

Incidence matrix according to Dynkin symbol

x5/2o3o5/3x5*b

.   . .   .    | 2400 |    3    6 |    3    6    3    3 |   1   3   3   1
---------------+------+-----------+---------------------+----------------
x   . .   .    |    2 | 3600    * |    2    2    0    0 |   1   2   1   0
.   . .   x    |    2 |    * 7200 |    0    1    1    1 |   0   1   1   1
---------------+------+-----------+---------------------+----------------
x5/2o .   .    |    5 |    5    0 | 1440    *    *    * |   1   1   0   0
x   . .   x    |    4 |    2    2 |    * 3600    *    * |   0   1   1   0
.   o .   x5*b |    5 |    0    5 |    *    * 1440    * |   0   1   0   1
.   . o5/3x    |    5 |    0    5 |    *    *    * 1440 |   0   0   1   1
---------------+------+-----------+---------------------+----------------
x5/2o3o   .    ♦   20 |   30    0 |   12    0    0    0 | 120   *   *   *
x5/2o .   x5*b ♦   60 |   60   60 |   12   30   12    0 |   * 120   *   *
x   . o5/3x    ♦   10 |    5   10 |    0    5    0    2 |   *   * 720   *
.   o3o5/3x5*b ♦   20 |    0   60 |    0    0   12   12 |   *   *   * 120

x5/2o3/2o5/2x5*b

.   .   .   .    | 2400 |    3    6 |    3    6    3    3 |   1   3   3   1
-----------------+------+-----------+---------------------+----------------
x   .   .   .    |    2 | 3600    * |    2    2    0    0 |   1   2   1   0
.   .   .   x    |    2 |    * 7200 |    0    1    1    1 |   0   1   1   1
-----------------+------+-----------+---------------------+----------------
x5/2o   .   .    |    5 |    5    0 | 1440    *    *    * |   1   1   0   0
x   .   .   x    |    4 |    2    2 |    * 3600    *    * |   0   1   1   0
.   o   .   x5*b |    5 |    0    5 |    *    * 1440    * |   0   1   0   1
.   .   o5/2x    |    5 |    0    5 |    *    *    * 1440 |   0   0   1   1
-----------------+------+-----------+---------------------+----------------
x5/2o3/2o   .    ♦   20 |   30    0 |   12    0    0    0 | 120   *   *   *
x5/2o   .   x5*b ♦   60 |   60   60 |   12   30   12    0 |   * 120   *   *
x   .   o5/2x    ♦   10 |    5   10 |    0    5    0    2 |   *   * 720   *
.   o3/2o5/2x5*b ♦   20 |    0   60 |    0    0   12   12 |   *   *   * 120

x5/3o3o5/2x5/4*b

.   . .   .      | 2400 |    3    6 |    3    6    3    3 |   1   3   3   1
-----------------+------+-----------+---------------------+----------------
x   . .   .      |    2 | 3600    * |    2    2    0    0 |   1   2   1   0
.   . .   x      |    2 |    * 7200 |    0    1    1    1 |   0   1   1   1
-----------------+------+-----------+---------------------+----------------
x5/3o .   .      |    5 |    5    0 | 1440    *    *    * |   1   1   0   0
x   . .   x      |    4 |    2    2 |    * 3600    *    * |   0   1   1   0
.   o .   x5/4*b |    5 |    0    5 |    *    * 1440    * |   0   1   0   1
.   . o5/2x      |    5 |    0    5 |    *    *    * 1440 |   0   0   1   1
-----------------+------+-----------+---------------------+----------------
x5/3o3o   .      ♦   20 |   30    0 |   12    0    0    0 | 120   *   *   *
x5/3o .   x5/4*b ♦   60 |   60   60 |   12   30   12    0 |   * 120   *   *
x   . o5/2x      ♦   10 |    5   10 |    0    5    0    2 |   *   * 720   *
.   o3o5/2x5/4*b ♦   20 |    0   60 |    0    0   12   12 |   *   *   * 120

x5/3o3/2o5/3x5/4*b

.   .   .   .      | 2400 |    3    6 |    3    6    3    3 |   1   3   3   1
-------------------+------+-----------+---------------------+----------------
x   .   .   .      |    2 | 3600    * |    2    2    0    0 |   1   2   1   0
.   .   .   x      |    2 |    * 7200 |    0    1    1    1 |   0   1   1   1
-------------------+------+-----------+---------------------+----------------
x5/3o   .   .      |    5 |    5    0 | 1440    *    *    * |   1   1   0   0
x   .   .   x      |    4 |    2    2 |    * 3600    *    * |   0   1   1   0
.   o   .   x5/4*b |    5 |    0    5 |    *    * 1440    * |   0   1   0   1
.   .   o5/3x      |    5 |    0    5 |    *    *    * 1440 |   0   0   1   1
-------------------+------+-----------+---------------------+----------------
x5/3o3/2o   .      ♦   20 |   30    0 |   12    0    0    0 | 120   *   *   *
x5/3o   .   x5/4*b ♦   60 |   60   60 |   12   30   12    0 |   * 120   *   *
x   .   o5/3x      ♦   10 |    5   10 |    0    5    0    2 |   *   * 720   *
.   o3/2o5/3x5/4*b ♦   20 |    0   60 |    0    0   12   12 |   *   *   * 120

or, identifying coincident vertices and edges:

 600 |   12 |   24   12   12   12 |   4  12  12   4
-----+------+---------------------+----------------
   2 | 3600 |    4    2    2    2 |   1   4   3   2
-----+------+---------------------+----------------
   4 |    4 | 3600    *    *    * |   0   1   1   0
   5 |    5 |    * 1440    *    * |   1   1   0   0
   5 |    5 |    *    * 1440    * |   0   1   0   1
   5 |    5 |    *    *    * 1440 |   0   0   1   1
-----+------+---------------------+----------------
♦ 20 |   30 |    0   12    0    0 | 120   *   *   *
♦ 60 |  120 |   30   12   12    0 |   * 120   *   *
♦ 10 |   15 |    5    0    0    2 |   *   * 720   *
♦ 20 |   60 |    0    0   12   12 |   *   *   * 120