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

This Grünbaumian polychoron happens to have axial vertex figures, in fact fv3/2of&#q, which coincide by 4 in a tetrahedral way. Thereby edges too can be seen to coincide by 3. Then seedatepthi belongs to the dattady regiment. As further the 2 classes of pentagons happens to coincide one by one, this polychoron moreover is exotic.

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

Incidence matrix according to Dynkin symbol

x5o3o5/4x5/2*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
---------------+------+-----------+---------------------+----------------
x5o .   .      |    5 |    5    0 | 1440    *    *    * |   1   1   0   0
x . .   x      |    4 |    2    2 |    * 3600    *    * |   0   1   1   0
. o .   x5/2*b |    5 |    0    5 |    *    * 1440    * |   0   1   0   1
. . o5/4x      |    5 |    0    5 |    *    *    * 1440 |   0   0   1   1
---------------+------+-----------+---------------------+----------------
x5o3o   .      ♦   20 |   30    0 |   12    0    0    0 | 120   *   *   *
x5o .   x5/2*b ♦   60 |   60   60 |   12   30   12    0 |   * 120   *   *
x . o5/4x      ♦   10 |    5   10 |    0    5    0    2 |   *   * 720   *
. o3o5/4x5/2*b ♦   20 |    0   60 |    0    0   12   12 |   *   *   * 120

x5o3/2o5x5/2*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
---------------+------+-----------+---------------------+----------------
x5o   . .      |    5 |    5    0 | 1440    *    *    * |   1   1   0   0
x .   . x      |    4 |    2    2 |    * 3600    *    * |   0   1   1   0
. o   . x5/2*b |    5 |    0    5 |    *    * 1440    * |   0   1   0   1
. .   o5x      |    5 |    0    5 |    *    *    * 1440 |   0   0   1   1
---------------+------+-----------+---------------------+----------------
x5o3/2o .      ♦   20 |   30    0 |   12    0    0    0 | 120   *   *   *
x5o   . x5/2*b ♦   60 |   60   60 |   12   30   12    0 |   * 120   *   *
x .   o5x      ♦   10 |    5   10 |    0    5    0    2 |   *   * 720   *
. o3/2o5x5/2*b ♦   20 |    0   60 |    0    0   12   12 |   *   *   * 120

x5/4o3o5x5/3*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
---------------+------+-----------+---------------------+----------------
x5/4o . .      |    5 |    5    0 | 1440    *    *    * |   1   1   0   0
x   . . x      |    4 |    2    2 |    * 3600    *    * |   0   1   1   0
.   o . x5/3*b |    5 |    0    5 |    *    * 1440    * |   0   1   0   1
.   . o5x      |    5 |    0    5 |    *    *    * 1440 |   0   0   1   1
---------------+------+-----------+---------------------+----------------
x5/4o3o .      ♦   20 |   30    0 |   12    0    0    0 | 120   *   *   *
x5/4o . x5/3*b ♦   60 |   60   60 |   12   30   12    0 |   * 120   *   *
x   . o5x      ♦   10 |    5   10 |    0    5    0    2 |   *   * 720   *
.   o3o5x5/3*b ♦   20 |    0   60 |    0    0   12   12 |   *   *   * 120

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