As abstract polytope 2gadtifady is isomorphic to 2sadtifady, thereby replacing pentagrams by pentagons and decagrams by decagons, resp. gaddid by saddid and gid by id.

Looks like a coincidic compound of 2 gadtifady copies. In fact, vertices coincide by 6, edges by 4, and all other elements by pairs.

Incidence matrix according to Dynkin symbol

x5/2o3x5/2o3*a5/3*c
.   . .   .         | 3600 |    4    4 |    2    4    2    2    2 |   2   1   2   1
--------------------+------+-----------+--------------------------+----------------
x   . .   .         |    2 | 7200    * |    1    1    1    0    0 |   1   1   1   0
.   . x   .         |    2 |    * 7200 |    0    1    0    1    1 |   1   0   1   1
--------------------+------+-----------+--------------------------+----------------
x5/2o .   .         |    5 |    5    0 | 1440    *    *    *    * |   1   1   0   0
x   . x   . *a5/3*c |   10 |    5    5 |    * 1440    *    *    * |   1   0   1   0
x   . .   o3*a      |    3 |    3    0 |    *    * 2400    *    * |   0   1   1   0
.   o3x   .         |    3 |    0    3 |    *    *    * 2400    * |   1   0   0   1
.   . x5/2o         |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
--------------------+------+-----------+--------------------------+----------------
x5/2o3x   . *a5/3*c ♦   60 |   60   60 |   12   12    0   20    0 | 120   *   *   *
x5/2o .   o3*a      ♦   30 |   60    0 |   12    0   20    0    0 |   * 120   *   *
x   . x5/2o3*a5/3*c ♦   60 |   60   60 |    0   12   20    0   12 |   *   * 120   *
.   o3x5/2o         ♦   30 |    0   60 |    0    0    0   20   12 |   *   *   * 120

or
.   . .   .            | 3600 |     8 |    4    4    4 |   4   2
-----------------------+------+-------+----------------+--------
x   . .   .          & |    2 | 14400 |    1    1    1 |   2   1
-----------------------+------+-------+----------------+--------
x5/2o .   .          & |    5 |     5 | 2880    *    * |   1   1
x   . x   . *a5/3*c    |   10 |    10 |    * 1440    * |   2   0
x   . .   o3*a       & |    3 |     3 |    *    * 4800 |   1   1
-----------------------+------+-------+----------------+--------
x5/2o3x   . *a5/3*c  & ♦   60 |   120 |   12   12   20 | 240   *
x5/2o .   o3*a       & ♦   30 |    60 |   12    0   20 |   * 240

x5/3o3/2x5/2o3*a5/3*c
.   .   .   .         | 3600 |    4    4 |    2    4    2    2    2 |   2   1   2   1
----------------------+------+-----------+--------------------------+----------------
x   .   .   .         |    2 | 7200    * |    1    1    1    0    0 |   1   1   1   0
.   .   x   .         |    2 |    * 7200 |    0    1    0    1    1 |   1   0   1   1
----------------------+------+-----------+--------------------------+----------------
x5/3o   .   .         |    5 |    5    0 | 1440    *    *    *    * |   1   1   0   0
x   .   x   . *a5/3*c |   10 |    5    5 |    * 1440    *    *    * |   1   0   1   0
x   .   .   o3*a      |    3 |    3    0 |    *    * 2400    *    * |   0   1   1   0
.   o3/2x   .         |    3 |    0    3 |    *    *    * 2400    * |   1   0   0   1
.   .   x5/2o         |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
----------------------+------+-----------+--------------------------+----------------
x5/3o3/2x   . *a5/3*c ♦   60 |   60   60 |   12   12    0   20    0 | 120   *   *   *
x5/3o   .   o3*a      ♦   30 |   60    0 |   12    0   20    0    0 |   * 120   *   *
x   .   x5/2o3*a5/3*c ♦   60 |   60   60 |    0   12   20    0   12 |   *   * 120   *
.   o3/2x5/2o         ♦   30 |    0   60 |    0    0    0   20   12 |   *   *   * 120

x5/3o3/2x5/3o3/2*a5/3*c
.   .   .   .           | 3600 |    4    4 |    2    4    2    2    2 |   2   1   2   1
------------------------+------+-----------+--------------------------+----------------
x   .   .   .           |    2 | 7200    * |    1    1    1    0    0 |   1   1   1   0
.   .   x   .           |    2 |    * 7200 |    0    1    0    1    1 |   1   0   1   1
------------------------+------+-----------+--------------------------+----------------
x5/3o   .   .           |    5 |    5    0 | 1440    *    *    *    * |   1   1   0   0
x   .   x   .   *a5/3*c |   10 |    5    5 |    * 1440    *    *    * |   1   0   1   0
x   .   .   o3/2*a      |    3 |    3    0 |    *    * 2400    *    * |   0   1   1   0
.   o3/2x   .           |    3 |    0    3 |    *    *    * 2400    * |   1   0   0   1
.   .   x5/3o           |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
------------------------+------+-----------+--------------------------+----------------
x5/3o3/2x   .   *a5/3*c ♦   60 |   60   60 |   12   12    0   20    0 | 120   *   *   *
x5/3o   .   o3/2*a      ♦   30 |   60    0 |   12    0   20    0    0 |   * 120   *   *
x   .   x5/3o3/2*a5/3*c ♦   60 |   60   60 |    0   12   20    0   12 |   *   * 120   *
.   o3/2x5/3o           ♦   30 |    0   60 |    0    0    0   20   12 |   *   *   * 120

or
.   .   .   .              | 3600 |     8 |    4    4    4 |   4   2
---------------------------+------+-------+----------------+--------
x   .   .   .            & |    2 | 14400 |    1    1    1 |   2   1
---------------------------+------+-------+----------------+--------
x5/3o   .   .            & |    5 |     5 | 2880    *    * |   1   1
x   .   x   .   *a5/3*c    |   10 |    10 |    * 1440    * |   2   0
x   .   .   o3/2*a       & |    3 |     3 |    *    * 4800 |   1   1
---------------------------+------+-------+----------------+--------
x5/3o3/2x   .   *a5/3*c  & ♦   60 |   120 |   12   12   20 | 240   *
x5/3o   .   o3/2*a       & ♦   30 |    60 |   12    0   20 |   * 240