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

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

Incidence matrix

x5x5/2o5o5/3*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
---------------+------+-----------+----------------+----------------
x5x   . .      |   10 |    5    5 | 1440    *    * |   1   1   0   0
x .   . o5/3*a |    5 |    5    0 |    * 1440    * |   0   1   1   0
. x5/2o .      |    5 |    0    5 |    *    * 1440 |   1   0   0   1
---------------+------+-----------+----------------+----------------
x5x5/2o .      ♦   60 |   30   60 |   12    0   12 | 120   *   *   *
x5x   . o5/3*a ♦   60 |   60   30 |   12   12    0 |   * 120   *   *
x .   o5o5/3*a ♦   12 |   30    0 |    0   12    0 |   *   * 120   *
. x5/2o5o      ♦   12 |    0   30 |    0    0   12 |   *   *   * 120

x5x5/2o5/4o5/2*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
-----------------+------+-----------+----------------+----------------
x5x   .   .      |   10 |    5    5 | 1440    *    * |   1   1   0   0
x .   .   o5/2*a |    5 |    5    0 |    * 1440    * |   0   1   1   0
. x5/2o   .      |    5 |    0    5 |    *    * 1440 |   1   0   0   1
-----------------+------+-----------+----------------+----------------
x5x5/2o   .      ♦   60 |   30   60 |   12    0   12 | 120   *   *   *
x5x   .   o5/2*a ♦   60 |   60   30 |   12   12    0 |   * 120   *   *
x .   o5/4o5/2*a ♦   12 |   30    0 |    0   12    0 |   *   * 120   *
. x5/2o5/4o      ♦   12 |    0   30 |    0    0   12 |   *   *   * 120

or
. .   .   .         | 1440 |   10 |   10   10 |  10   2
--------------------+------+------+-----------+--------
x .   .   .       & |    2 | 7200 |    2    2 |   3   1
--------------------+------+------+-----------+--------
x5x   .   .         |   10 |   10 | 1440    * |   2   0
x .   .   o5/2*a  & |    5 |    5 |    * 2880 |   1   1
--------------------+------+------+-----------+--------
x5x5/2o   .       & ♦   60 |   90 |   12   12 | 240   *
x .   o5/4o5/2*a  & ♦   12 |   30 |    0   12 |   * 240

x5x5/3o5/4o5/3*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
-----------------+------+-----------+----------------+----------------
x5x   .   .      |   10 |    5    5 | 1440    *    * |   1   1   0   0
x .   .   o5/3*a |    5 |    5    0 |    * 1440    * |   0   1   1   0
. x5/3o   .      |    5 |    0    5 |    *    * 1440 |   1   0   0   1
-----------------+------+-----------+----------------+----------------
x5x5/3o   .      ♦   60 |   30   60 |   12    0   12 | 120   *   *   *
x5x   .   o5/3*a ♦   60 |   60   30 |   12   12    0 |   * 120   *   *
x .   o5/4o5/3*a ♦   12 |   30    0 |    0   12    0 |   *   * 120   *
. x5/3o5/4o      ♦   12 |    0   30 |    0    0   12 |   *   *   * 120

or
. .   .   .         | 1440 |   10 |   10   10 |  10   2
--------------------+------+------+-----------+--------
x .   .   .       & |    2 | 7200 |    2    2 |   3   1
--------------------+------+------+-----------+--------
x5x   .   .         |   10 |   10 | 1440    * |   2   0
x .   .   o5/3*a  & |    5 |    5 |    * 2880 |   1   1
--------------------+------+------+-----------+--------
x5x5/3o   .       & ♦   60 |   90 |   12   12 | 240   *
x .   o5/4o5/3*a  & ♦   12 |   30 |    0   12 |   * 240