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

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

Incidence matrix according to Dynkin symbol

x5o3/2x5o3/2*a5*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
------------------+------+-----------+--------------------------+----------------
x5o   . .         |    5 |    5    0 | 1440    *    *    *    * |   1   1   0   0
x .   x .   *a5*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
. .   x5o         |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
------------------+------+-----------+--------------------------+----------------
x5o3/2x .   *a5*c ♦   60 |   60   60 |   12   12    0   20    0 | 120   *   *   *
x5o   . o3/2*a    ♦   30 |   60    0 |   12    0   20    0    0 |   * 120   *   *
x .   x5o3/2*a5*c ♦   60 |   60   60 |    0   12   20    0   12 |   *   * 120   *
. o3/2x5o         ♦   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
---------------------+------+-------+----------------+--------
x5o   . .          & |    5 |     5 | 2880    *    * |   1   1
x .   x .   *a5*c    |   10 |    10 |    * 1440    * |   2   0
x .   . o3/2*a     & |    3 |     3 |    *    * 4800 |   1   1
---------------------+------+-------+----------------+--------
x5o3/2x .   *a5*c  & ♦   60 |   120 |   12   12   20 | 240   *
x5o   . o3/2*a     & ♦   30 |    60 |   12    0   20 |   * 240

x5o3/2x5/4o3*a5*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
------------------+------+-----------+--------------------------+----------------
x5o   .   .       |    5 |    5    0 | 1440    *    *    *    * |   1   1   0   0
x .   x   . *a5*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
. .   x5/4o       |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
------------------+------+-----------+--------------------------+----------------
x5o3/2x   . *a5*c ♦   60 |   60   60 |   12   12    0   20    0 | 120   *   *   *
x5o   .   o3*a    ♦   30 |   60    0 |   12    0   20    0    0 |   * 120   *   *
x .   x5/4o3*a5*c ♦   60 |   60   60 |    0   12   20    0   12 |   *   * 120   *
. o3/2x5/4o       ♦   30 |    0   60 |    0    0    0   20   12 |   *   *   * 120

x5/4o3x5/4o3*a5*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
------------------+------+-----------+--------------------------+----------------
x5/4o .   .       |    5 |    5    0 | 1440    *    *    *    * |   1   1   0   0
x   . x   . *a5*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
.   . x5/4o       |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
------------------+------+-----------+--------------------------+----------------
x5/4o3x   . *a5*c ♦   60 |   60   60 |   12   12    0   20    0 | 120   *   *   *
x5/4o .   o3*a    ♦   30 |   60    0 |   12    0   20    0    0 |   * 120   *   *
x   . x5/4o3*a5*c ♦   60 |   60   60 |    0   12   20    0   12 |   *   * 120   *
.   o3x5/4o       ♦   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
---------------------+------+-------+----------------+--------
x5/4o .   .        & |    5 |     5 | 2880    *    * |   1   1
x   . x   . *a5*c    |   10 |    10 |    * 1440    * |   2   0
x   . .   o3*a     & |    3 |     3 |    *    * 4800 |   1   1
---------------------+------+-------+----------------+--------
x5/4o3x   . *a5*c  & ♦   60 |   120 |   12   12   20 | 240   *
x5/4o .   o3*a     & ♦   30 |    60 |   12    0   20 |   * 240