Looks like a compound of 2 small tripesic hecatonicosachora (sitphi), and indeed vertices coincide by 6, all other elements by 2.

As abstract polytope sitphi is isomorphic to gitphi, thereby replacing the decagons by decagrams and pentagrams by pentagons, resp. replacing tigid by quit sissid.

Incidence matrix according to Dynkin symbol

o5/2x5x5/2o

.   . .   . | 3600 |    2    2 |   1    4   1 |   2   2
------------+------+-----------+--------------+--------
.   x .   . |    2 | 3600    * |   1    2   0 |   2   1
.   . x   . |    2 |    * 3600 |   0    2   1 |   1   2
------------+------+-----------+--------------+--------
o5/2x .   . |    5 |    5    0 | 720    *   * |   2   0
.   x5x   . |   10 |    5    5 |   * 1440   * |   1   1
.   . x5/2o |    5 |    0    5 |   *    * 720 |   0   2
------------+------+-----------+--------------+--------
o5/2x5x   . ♦   60 |   60   30 |  12   12   0 | 120   *
.   x5x5/2o ♦   60 |   30   60 |   0   12  12 |   * 120

or
.   . .   .    | 3600 |    4 |    2    4 |   4
---------------+------+------+-----------+----
.   x .   .  & |    2 | 7200 |    1    2 |   3
---------------+------+------+-----------+----
o5/2x .   .  & |    5 |    5 | 1440    * |   2
.   x5x   .    |   10 |   10 |    * 1440 |   2
---------------+------+------+-----------+----
o5/2x5x   .  & ♦   60 |   90 |   12   12 | 240

o5/2x5x5/3o

.   . .   . | 3600 |    2    2 |   1    4   1 |   2   2
------------+------+-----------+--------------+--------
.   x .   . |    2 | 3600    * |   1    2   0 |   2   1
.   . x   . |    2 |    * 3600 |   0    2   1 |   1   2
------------+------+-----------+--------------+--------
o5/2x .   . |    5 |    5    0 | 720    *   * |   2   0
.   x5x   . |   10 |    5    5 |   * 1440   * |   1   1
.   . x5/3o |    5 |    0    5 |   *    * 720 |   0   2
------------+------+-----------+--------------+--------
o5/2x5x   . ♦   60 |   60   30 |  12   12   0 | 120   *
.   x5x5/3o ♦   60 |   30   60 |   0   12  12 |   * 120

o5/3x5x5/3o

.   . .   . | 3600 |    2    2 |   1    4   1 |   2   2
------------+------+-----------+--------------+--------
.   x .   . |    2 | 3600    * |   1    2   0 |   2   1
.   . x   . |    2 |    * 3600 |   0    2   1 |   1   2
------------+------+-----------+--------------+--------
o5/3x .   . |    5 |    5    0 | 720    *   * |   2   0
.   x5x   . |   10 |    5    5 |   * 1440   * |   1   1
.   . x5/3o |    5 |    0    5 |   *    * 720 |   0   2
------------+------+-----------+--------------+--------
o5/3x5x   . ♦   60 |   60   30 |  12   12   0 | 120   *
.   x5x5/3o ♦   60 |   30   60 |   0   12  12 |   * 120

or
.   . .   .    | 3600 |    4 |    2    4 |   4
---------------+------+------+-----------+----
.   x .   .  & |    2 | 7200 |    1    2 |   3
---------------+------+------+-----------+----
o5/3x .   .  & |    5 |    5 | 1440    * |   2
.   x5x   .    |   10 |   10 |    * 1440 |   2
---------------+------+------+-----------+----
o5/3x5x   .  & ♦   60 |   90 |   12   12 | 240