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

As abstract polytope 2ridditdy is automorphic, thereby replacing pentagons by pentagrams while ditdid and raded are automorphic too.

Incidence matrix according to Dynkin symbol

o5x5/2o5x5/2*a3/2*c

. .   . .           | 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
--------------------+------+-----------+--------------------------+----------------
o5x   . .           |    5 |    5    0 | 1440    *    *    *    * |   1   1   0   0
o .   . x5/2*a      |    5 |    0    5 |    * 1440    *    *    * |   0   1   1   0
. x5/2o .           |    5 |    5    0 |    *    * 1440    *    * |   1   0   0   1
. x   . x           |    4 |    2    2 |    *    *    * 3600    * |   0   1   0   1
. .   o5x           |    5 |    0    5 |    *    *    *    * 1440 |   0   0   1   1
--------------------+------+-----------+--------------------------+----------------
o5x5/2o .   *a3/2*c ♦   20 |   60    0 |   12    0   12    0    0 | 120   *   *   *
o5x   . x5/2*a      ♦   60 |   60   60 |   12   12    0   30    0 |   * 120   *   *
o .   o5x5/2*a3/2*c ♦   20 |    0   60 |    0   12    0    0   12 |   *   * 120   *
. x5/2o5x           ♦   60 |   60   60 |    0    0   12   30   12 |   *   *   * 120