Looks like a compound of a sishi with gridixhi. The vertex figure is v3x3/2o5*a, a facetting of doe. Edges coincide by 3 and pentagrams come in coincident pairs.

As abstract polytope sishi+gridixhi is isomorphic to gaghi+sridixhi, thereby replacing pentagrams by pentagons, resp. sidtid by gidtid and sissid by gad.

Incidence matrix according to Dynkin symbol

o3o5o5/2x3/2*a3/2*c

. . .   .           | 120 |   60 |   60   60 |  20  20  12
--------------------+-----+------+-----------+------------
. . .   x           |   2 | 3600 |    2    2 |   1   2   1
--------------------+-----+------+-----------+------------
o . .   x3/2*a      |   3 |    3 | 2400    * |   1   1   0
. . o5/2x           |   5 |    5 |    * 1440 |   0   1   1
--------------------+-----+------+-----------+------------
o3o .   x3/2*a      ♦   4 |    6 |    4    0 | 600   *   *
o . o5/2x3/2*a3/2*c ♦  20 |   60 |   20   12 |   * 120   *
. o5o5/2x           ♦  12 |   30 |    0   12 |   *   * 120

o3o5o5/3x3*a3/2*c

. . .   .         | 120 |   60 |   60   60 |  20  20  12
------------------+-----+------+-----------+------------
. . .   x         |   2 | 3600 |    2    2 |   1   2   1
------------------+-----+------+-----------+------------
o . .   x3*a      |   3 |    3 | 2400    * |   1   1   0
. . o5/3x         |   5 |    5 |    * 1440 |   0   1   1
------------------+-----+------+-----------+------------
o3o .   x3*a      ♦   4 |    6 |    4    0 | 600   *   *
o . o5/3x3*a3/2*c ♦  20 |   60 |   20   12 |   * 120   *
. o5o5/3x         ♦  12 |   30 |    0   12 |   *   * 120

o3o5/4o5/2x3*a3*c

. .   .   .       | 120 |   60 |   60   60 |  20  20  12
------------------+-----+------+-----------+------------
. .   .   x       |   2 | 3600 |    2    2 |   1   2   1
------------------+-----+------+-----------+------------
o .   .   x3*a    |   3 |    3 | 2400    * |   1   1   0
. .   o5/2x       |   5 |    5 |    * 1440 |   0   1   1
------------------+-----+------+-----------+------------
o3o   .   x3*a    ♦   4 |    6 |    4    0 | 600   *   *
o .   o5/2x3*a3*c ♦  20 |   60 |   20   12 |   * 120   *
. o5/4o5/2x       ♦  12 |   30 |    0   12 |   *   * 120

o3o5/4o5/3x3/2*a3*c

. .   .   .         | 120 |   60 |   60   60 |  20  20  12
--------------------+-----+------+-----------+------------
. .   .   x         |   2 | 3600 |    2    2 |   1   2   1
--------------------+-----+------+-----------+------------
o .   .   x3/2*a    |   3 |    3 | 2400    * |   1   1   0
. .   o5/3x         |   5 |    5 |    * 1440 |   0   1   1
--------------------+-----+------+-----------+------------
o3o   .   x3/2*a    ♦   4 |    6 |    4    0 | 600   *   *
o .   o5/3x3/2*a3*c ♦  20 |   60 |   20   12 |   * 120   *
. o5/4o5/3x         ♦  12 |   30 |    0   12 |   *   * 120

o3/2o5o5/2x3*a3*c

.   . .   .       | 120 |   60 |   60   60 |  20  20  12
------------------+-----+------+-----------+------------
.   . .   x       |   2 | 3600 |    2    2 |   1   2   1
------------------+-----+------+-----------+------------
o   . .   x3*a    |   3 |    3 | 2400    * |   1   1   0
.   . o5/2x       |   5 |    5 |    * 1440 |   0   1   1
------------------+-----+------+-----------+------------
o3/2o .   x3*a    ♦   4 |    6 |    4    0 | 600   *   *
o   . o5/2x3*a3*c ♦  20 |   60 |   20   12 |   * 120   *
.   o5o5/2x       ♦  12 |   30 |    0   12 |   *   * 120

o3/2o5o5/3x3/2*a3*c

.   . .   .         | 120 |   60 |   60   60 |  20  20  12
--------------------+-----+------+-----------+------------
.   . .   x         |   2 | 3600 |    2    2 |   1   2   1
--------------------+-----+------+-----------+------------
o   . .   x3/2*a    |   3 |    3 | 2400    * |   1   1   0
.   . o5/3x         |   5 |    5 |    * 1440 |   0   1   1
--------------------+-----+------+-----------+------------
o3/2o .   x3/2*a    ♦   4 |    6 |    4    0 | 600   *   *
o   . o5/3x3/2*a3*c ♦  20 |   60 |   20   12 |   * 120   *
.   o5o5/3x         ♦  12 |   30 |    0   12 |   *   * 120

o3/2o5/4o5/2x3/2*a3/2*c

.   .   .   .           | 120 |   60 |   60   60 |  20  20  12
------------------------+-----+------+-----------+------------
.   .   .   x           |   2 | 3600 |    2    2 |   1   2   1
------------------------+-----+------+-----------+------------
o   .   .   x3/2*a      |   3 |    3 | 2400    * |   1   1   0
.   .   o5/2x           |   5 |    5 |    * 1440 |   0   1   1
------------------------+-----+------+-----------+------------
o3/2o   .   x3/2*a      ♦   4 |    6 |    4    0 | 600   *   *
o   .   o5/2x3/2*a3/2*c ♦  20 |   60 |   20   12 |   * 120   *
.   o5/4o5/2x           ♦  12 |   30 |    0   12 |   *   * 120

o3/2o5/4o5/3x3*a3/2*c

.   .   .   .         | 120 |   60 |   60   60 |  20  20  12
----------------------+-----+------+-----------+------------
.   .   .   x         |   2 | 3600 |    2    2 |   1   2   1
----------------------+-----+------+-----------+------------
o   .   .   x3*a      |   3 |    3 | 2400    * |   1   1   0
.   .   o5/3x         |   5 |    5 |    * 1440 |   0   1   1
----------------------+-----+------+-----------+------------
o3/2o   .   x3*a      ♦   4 |    6 |    4    0 | 600   *   *
o   .   o5/3x3*a3/2*c ♦  20 |   60 |   20   12 |   * 120   *
.   o5/4o5/3x         ♦  12 |   30 |    0   12 |   *   * 120