Looks like a completely coincident compound of 2 copies of sidditdy, in fact all elements coincide by 2.

As abstract polytope 2sidditdy is isomorphic to 2gidditdy, thereby replacing pentagrams by pentagons and decagons by decagrams resp. replacing sidtid by gidtid and sidditdid by gidditdid.

Incidence matrix according to Dynkin symbol

o3x5/2o3/2x5/3*a3*c *b5*d

. .   .   .               | 2400 |    6    6 |    3    3    3    6    3 |   1   3   1   3
--------------------------+------+-----------+--------------------------+----------------
. x   .   .               |    2 | 7200    * |    1    0    1    1    0 |   1   1   0   1
. .   .   x               |    2 |    * 7200 |    0    1    0    1    1 |   0   1   1   1
--------------------------+------+-----------+--------------------------+----------------
o3x   .   .               |    3 |    3    0 | 2400    *    *    *    * |   1   1   0   0
o .   .   x5/3*a          |    5 |    0    5 |    * 1440    *    *    * |   0   1   1   0
. x5/2o   .               |    5 |    5    0 |    *    * 1440    *    * |   1   0   0   1
. x   .   x         *b5*d |   10 |    5    5 |    *    *    * 1440    * |   0   1   0   1
. .   o3/2x               |    3 |    0    3 |    *    *    *    * 2400 |   0   0   1   1
--------------------------+------+-----------+--------------------------+----------------
o3x5/2o   .   *a3*c       ♦   20 |   60    0 |   20    0   12    0    0 | 120   *   *   *
o3x   .   x5/3*a    *b5*d ♦   60 |   60   60 |   20   12    0   12    0 |   * 120   *   *
o .   o3/2x5/3*a3*c       ♦   20 |    0   60 |    0   12    0    0   20 |   *   * 120   *
. x5/2o3/2x         *b5*d ♦   60 |   60   60 |    0    0   12   12   20 |   *   *   * 120