Looks like a compound of 2 gashi with vertices and edges identified, while faces and cells coincide by pairs.

As abstract polytope 2gashi is isomorphic to 2gohi, thereby replacing pentagrams by pentagons, resp. replacing sissid by gad, resp. replacing 2gad vertex figures by 2sissid ones.

Incidence matrix according to Dynkin symbol

x5/2o5o5o5/4*b

.   . . .      | 120 ♦  12 |   60 |  12  12
---------------+-----+-----+------+--------
x   . . .      |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/2o . .      |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/2o5o .      ♦  12 |  30 |   12 | 120   *
x5/2o . o5/4*b ♦  12 |  30 |   12 |   * 120

x5/2o5o5/4o5*b

.   . .   .    | 120 ♦  12 |   60 |  12  12
---------------+-----+-----+------+--------
x   . .   .    |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/2o .   .    |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/2o5o   .    ♦  12 |  30 |   12 | 120   *
x5/2o .   o5*b ♦  12 |  30 |   12 |   * 120

or
.   . .   .       | 120 ♦  12 |   60 |  24
------------------+-----+-----+------+----
x   . .   .       |   2 | 720 |   10 |  10
------------------+-----+-----+------+----
x5/2o .   .       |   5 |   5 | 1440 |   2
------------------+-----+-----+------+----
x5/2o5o   .     & ♦  12 |  30 |   12 | 240

x5/2o5/4o5/4o5/4*b

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

or
.   .   .   .         | 120 ♦  12 |   60 |  24
----------------------+-----+-----+------+----
x   .   .   .         |   2 | 720 |   10 |  10
----------------------+-----+-----+------+----
x5/2o   .   .         |   5 |   5 | 1440 |   2
----------------------+-----+-----+------+----
x5/2o5/4o   .       & ♦  12 |  30 |   12 | 240

x5/3o5o5o5/4*b

.   . . .      | 120 ♦  12 |   60 |  12  12
---------------+-----+-----+------+--------
x   . . .      |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/3o . .      |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/3o5o .      ♦  12 |  30 |   12 | 120   *
x5/3o . o5/4*b ♦  12 |  30 |   12 |   * 120

x5/3o5o5/4o5*b

.   . .   .    | 120 ♦  12 |   60 |  12  12
---------------+-----+-----+------+--------
x   . .   .    |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/3o .   .    |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/3o5o   .    ♦  12 |  30 |   12 | 120   *
x5/3o .   o5*b ♦  12 |  30 |   12 |   * 120

or
.   . .   .       | 120 ♦  12 |   60 |  24
------------------+-----+-----+------+----
x   . .   .       |   2 | 720 |   10 |  10
------------------+-----+-----+------+----
x5/3o .   .       |   5 |   5 | 1440 |   2
------------------+-----+-----+------+----
x5/3o5o   .     & ♦  12 |  30 |   12 | 240

x5/3o5/4o5/4o5/4*b

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

or
.   .   .   .         | 120 ♦  12 |   60 |  24
----------------------+-----+-----+------+----
x   .   .   .         |   2 | 720 |   10 |  10
----------------------+-----+-----+------+----
x5/3o   .   .         |   5 |   5 | 1440 |   2
----------------------+-----+-----+------+----
x5/3o5/4o   .       & ♦  12 |  30 |   12 | 240