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

As abstract polytope 2spapivady is isomorphic to 2giprapivady, thereby replacing pentagons by pentagrams and decagrams by decagons, resp. replacing gad by sissid and quit sissid by tigid.

Incidence matrix

x5/3x5o5/2o5*a

.   . .   .    | 1440 |    5    5 |   10    5    5 |   5   5   1   1
---------------+------+-----------+----------------+----------------
x   . .   .    |    2 | 3600    * |    2    2    0 |   1   2   1   0
.   x .   .    |    2 |    * 3600 |    2    0    2 |   2   1   0   1
---------------+------+-----------+----------------+----------------
x5/3x .   .    |   10 |    5    5 | 1440    *    * |   1   1   0   0
x   . .   o5*a |    5 |    5    0 |    * 1440    * |   0   1   1   0
.   x5o   .    |    5 |    0    5 |    *    * 1440 |   1   0   0   1
---------------+------+-----------+----------------+----------------
x5/3x5o   .    ♦   60 |   30   60 |   12    0   12 | 120   *   *   *
x5/3x .   o5*a ♦   60 |   60   30 |   12   12    0 |   * 120   *   *
x   . o5/2o5*a ♦   12 |   30    0 |    0   12    0 |   *   * 120   *
.   x5o5/2o    ♦   12 |    0   30 |    0    0   12 |   *   *   * 120

or
.   . .   .       | 1440 |   10 |   10   10 |  10   2
------------------+------+------+-----------+--------
x   . .   .     & |    2 | 7200 |    2    2 |   3   1
------------------+------+------+-----------+--------
x5/3x .   .       |   10 |   10 | 1440    * |   2   0
x   . .   o5*a  & |    5 |    5 |    * 2880 |   1   1
------------------+------+------+-----------+--------
x5/3x5o   .     & ♦   60 |   90 |   12   12 | 240   *
x   . o5/2o5*a  & ♦   12 |   30 |    0   12 |   * 240

x5/3x5o5/3o5/4*a

.   . .   .      | 1440 |    5    5 |   10    5    5 |   5   5   1   1
-----------------+------+-----------+----------------+----------------
x   . .   .      |    2 | 3600    * |    2    2    0 |   1   2   1   0
.   x .   .      |    2 |    * 3600 |    2    0    2 |   2   1   0   1
-----------------+------+-----------+----------------+----------------
x5/3x .   .      |   10 |    5    5 | 1440    *    * |   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
-----------------+------+-----------+----------------+----------------
x5/3x5o   .      ♦   60 |   30   60 |   12    0   12 | 120   *   *   *
x5/3x .   o5/4*a ♦   60 |   60   30 |   12   12    0 |   * 120   *   *
x   . o5/3o5/4*a ♦   12 |   30    0 |    0   12    0 |   *   * 120   *
.   x5o5/3o      ♦   12 |    0   30 |    0    0   12 |   *   *   * 120

x5/3x5/4o5/2o5/4*a

.   .   .   .      | 1440 |    5    5 |   10    5    5 |   5   5   1   1
-------------------+------+-----------+----------------+----------------
x   .   .   .      |    2 | 3600    * |    2    2    0 |   1   2   1   0
.   x   .   .      |    2 |    * 3600 |    2    0    2 |   2   1   0   1
-------------------+------+-----------+----------------+----------------
x5/3x   .   .      |   10 |    5    5 | 1440    *    * |   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
-------------------+------+-----------+----------------+----------------
x5/3x5/4o   .      ♦   60 |   30   60 |   12    0   12 | 120   *   *   *
x5/3x   .   o5/4*a ♦   60 |   60   30 |   12   12    0 |   * 120   *   *
x   .   o5/2o5/4*a ♦   12 |   30    0 |    0   12    0 |   *   * 120   *
.   x5/4o5/2o      ♦   12 |    0   30 |    0    0   12 |   *   *   * 120

or
.   .   .   .         | 1440 |   10 |   10   10 |  10   2
----------------------+------+------+-----------+--------
x   .   .   .       & |    2 | 7200 |    2    2 |   3   1
----------------------+------+------+-----------+--------
x5/3x   .   .         |   10 |   10 | 1440    * |   2   0
x   .   .   o5/4*a  & |    5 |    5 |    * 2880 |   1   1
----------------------+------+------+-----------+--------
x5/3x5/4o   .       & ♦   60 |   90 |   12   12 | 240   *
x   .   o5/2o5/4*a  & ♦   12 |   30 |    0   12 |   * 240