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

As abstract polytope 2firsashi is isomorphic to 2firgaghi, thereby replacing pentagons by pentagrams, resp. replacing doe by gissid and ti by tiggy.

Incidence matrix according to Dynkin symbol

x3x5o3o5/4*a

. . . .      | 2400 |    3    3 |    6    3    3 |   3   3   1   1
-------------+------+-----------+----------------+----------------
x . . .      |    2 | 3600    * |    2    2    0 |   1   2   1   0
. x . .      |    2 |    * 3600 |    2    0    2 |   2   1   0   1
-------------+------+-----------+----------------+----------------
x3x . .      |    6 |    3    3 | 2400    *    * |   1   1   0   0
x . . o5/4*a |    5 |    5    0 |    * 1440    * |   0   1   1   0
. x5o .      |    5 |    0    5 |    *    * 1440 |   1   0   0   1
-------------+------+-----------+----------------+----------------
x3x5o .      ♦   60 |   30   60 |   20    0   12 | 120   *   *   *
x3x . o5/4*a ♦   60 |   60   30 |   20   12    0 |   * 120   *   *
x . o3o5/4*a ♦   20 |   30    0 |    0   12    0 |   *   * 120   *
. x5o3o      ♦   20 |    0   30 |    0    0   12 |   *   *   * 120

x3x5o3/2o5*a

. . .   .    | 2400 |    3    3 |    6    3    3 |   3   3   1   1
-------------+------+-----------+----------------+----------------
x . .   .    |    2 | 3600    * |    2    2    0 |   1   2   1   0
. x .   .    |    2 |    * 3600 |    2    0    2 |   2   1   0   1
-------------+------+-----------+----------------+----------------
x3x .   .    |    6 |    3    3 | 2400    *    * |   1   1   0   0
x . .   o5*a |    5 |    5    0 |    * 1440    * |   0   1   1   0
. x5o   .    |    5 |    0    5 |    *    * 1440 |   1   0   0   1
-------------+------+-----------+----------------+----------------
x3x5o   .    ♦   60 |   30   60 |   20    0   12 | 120   *   *   *
x3x .   o5*a ♦   60 |   60   30 |   20   12    0 |   * 120   *   *
x . o3/2o5*a ♦   20 |   30    0 |    0   12    0 |   *   * 120   *
. x5o3/2o    ♦   20 |    0   30 |    0    0   12 |   *   *   * 120

or
. . .   .       | 2400 |    6 |    6    6 |   6   2
----------------+------+------+-----------+--------
x . .   .     & |    2 | 7200 |    2    2 |   3   1
----------------+------+------+-----------+--------
x3x .   .       |    6 |    6 | 2400    * |   2   0
x . .   o5*a  & |    5 |    5 |    * 2880 |   1   1
----------------+------+------+-----------+--------
x3x5o   .     & ♦   60 |   90 |   20   12 | 240   *
x . o3/2o5*a  & ♦   20 |   30 |    0   12 |   * 240

x3x5/4o3/2o5/4*a

. .   .   .      | 2400 |    3    3 |    6    3    3 |   3   3   1   1
-----------------+------+-----------+----------------+----------------
x .   .   .      |    2 | 3600    * |    2    2    0 |   1   2   1   0
. x   .   .      |    2 |    * 3600 |    2    0    2 |   2   1   0   1
-----------------+------+-----------+----------------+----------------
x3x   .   .      |    6 |    3    3 | 2400    *    * |   1   1   0   0
x .   .   o5/4*a |    5 |    5    0 |    * 1440    * |   0   1   1   0
. x5/4o   .      |    5 |    0    5 |    *    * 1440 |   1   0   0   1
-----------------+------+-----------+----------------+----------------
x3x5/4o   .      ♦   60 |   30   60 |   20    0   12 | 120   *   *   *
x3x   .   o5/4*a ♦   60 |   60   30 |   20   12    0 |   * 120   *   *
x .   o3/2o5/4*a ♦   20 |   30    0 |    0   12    0 |   *   * 120   *
. x5/4o3/2o      ♦   20 |    0   30 |    0    0   12 |   *   *   * 120

or
. .   .   .         | 2400 |    6 |    6    6 |   6   2
--------------------+------+------+-----------+--------
x .   .   .       & |    2 | 7200 |    2    2 |   3   1
--------------------+------+------+-----------+--------
x3x   .   .         |    6 |    6 | 2400    * |   2   0
x .   .   o5/4*a  & |    5 |    5 |    * 2880 |   1   1
--------------------+------+------+-----------+--------
x3x5/4o   .       & ♦   60 |   90 |   20   12 | 240   *
x .   o3/2o5/4*a  & ♦   20 |   30 |    0   12 |   * 240