Looks like a compound of a gaghi with sridixhi. The vertex figure is f3x3/2o5/3*a, a facetting of doe. Edges coincide by 3 and pentagons come in coincident pairs.

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

Incidence matrix according to Dynkin symbol

o3o5/2o5x3/2*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
. .   o5x         |   5 |    5 |    * 1440 |   0   1   1
------------------+-----+------+-----------+------------
o3o   . x3/2*a    ♦   4 |    6 |    4    0 | 600   *   *
o .   o5x3/2*a3*c ♦  20 |   60 |   20   12 |   * 120   *
. o5/2o5x         ♦  12 |   30 |    0   12 |   *   * 120

o3o5/2o5/4x3*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
. .   o5/4x       |   5 |    5 |    * 1440 |   0   1   1
------------------+-----+------+-----------+------------
o3o   .   x3*a    ♦   4 |    6 |    4    0 | 600   *   *
o .   o5/4x3*a3*c ♦  20 |   60 |   20   12 |   * 120   *
. o5/2o5/4x       ♦  12 |   30 |    0   12 |   *   * 120

o3o5/3o5x3*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
. .   o5x         |   5 |    5 |    * 1440 |   0   1   1
------------------+-----+------+-----------+------------
o3o   . x3*a      ♦   4 |    6 |    4    0 | 600   *   *
o .   o5x3*a3/2*c ♦  20 |   60 |   20   12 |   * 120   *
. o5/3o5x         ♦  12 |   30 |    0   12 |   *   * 120

o3o5/3o5/4x3/2*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
. .   o5/4x           |   5 |    5 |    * 1440 |   0   1   1
----------------------+-----+------+-----------+------------
o3o   .   x3/2*a      ♦   4 |    6 |    4    0 | 600   *   *
o .   o5/4x3/2*a3/2*c ♦  20 |   60 |   20   12 |   * 120   *
. o5/3o5/4x           ♦  12 |   30 |    0   12 |   *   * 120

o3/2o5/2o5x3*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
.   .   o5x         |   5 |    5 |    * 1440 |   0   1   1
--------------------+-----+------+-----------+------------
o3/2o   . x3*a      ♦   4 |    6 |    4    0 | 600   *   *
o   .   o5x3*a3/2*c ♦  20 |   60 |   20   12 |   * 120   *
.   o5/2o5x         ♦  12 |   30 |    0   12 |   *   * 120

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

o3/2o5/3o5x3/2*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
.   .   o5x         |   5 |    5 |    * 1440 |   0   1   1
--------------------+-----+------+-----------+------------
o3/2o   . x3/2*a    ♦   4 |    6 |    4    0 | 600   *   *
o   .   o5x3/2*a3*c ♦  20 |   60 |   20   12 |   * 120   *
.   o5/3o5x         ♦  12 |   30 |    0   12 |   *   * 120

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