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

As abstract polytope 2gitphi is isomorphic to 2sitphi, thereby replacing the decagrams by decagons and pentagons by pentagrams, resp. replacing quit sissid by tigid.

Incidence matrix according to Dynkin symbol

o5x5/3x5o

. .   . . | 3600 |    2    2 |   1    4   1 |   2   2
----------+------+-----------+--------------+--------
. x   . . |    2 | 3600    * |   1    2   0 |   2   1
. .   x . |    2 |    * 3600 |   0    2   1 |   1   2
----------+------+-----------+--------------+--------
o5x   . . |    5 |    5    0 | 720    *   * |   2   0
. x5/3x . |   10 |    5    5 |   * 1440   * |   1   1
. .   x5o |    5 |    0    5 |   *    * 720 |   0   2
----------+------+-----------+--------------+--------
o5x5/3x . ♦   60 |   60   30 |  12   12   0 | 120   *
. x5/3x5o ♦   60 |   30   60 |   0   12  12 |   * 120

or
. .   . .    | 3600 |    4 |    2    4 |   4
-------------+------+------+-----------+----
. x   . .  & |    2 | 7200 |    1    2 |   3
-------------+------+------+-----------+----
o5x   . .  & |    5 |    5 | 1440    * |   2
. x5/3x .    |   10 |   10 |    * 1440 |   2
-------------+------+------+-----------+----
o5x5/3x .  & ♦   60 |   90 |   12   12 | 240

o5x5/3x5/4o

. .   .   . | 3600 |    2    2 |   1    4   1 |   2   2
------------+------+-----------+--------------+--------
. x   .   . |    2 | 3600    * |   1    2   0 |   2   1
. .   x   . |    2 |    * 3600 |   0    2   1 |   1   2
------------+------+-----------+--------------+--------
o5x   .   . |    5 |    5    0 | 720    *   * |   2   0
. x5/3x   . |   10 |    5    5 |   * 1440   * |   1   1
. .   x5/4o |    5 |    0    5 |   *    * 720 |   0   2
------------+------+-----------+--------------+--------
o5x5/3x   . ♦   60 |   60   30 |  12   12   0 | 120   *
. x5/3x5/4o ♦   60 |   30   60 |   0   12  12 |   * 120

o5/4x5/3x5/4o

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

or
.   .   .   .    | 3600 |    4 |    2    4 |   4
-----------------+------+------+-----------+----
.   x   .   .  & |    2 | 7200 |    1    2 |   3
-----------------+------+------+-----------+----
o5/4x   .   .  & |    5 |    5 | 1440    * |   2
.   x5/3x   .    |   10 |   10 |    * 1440 |   2
-----------------+------+------+-----------+----
o5/4x5/3x   .  & ♦   60 |   90 |   12   12 | 240