Looks like a compound of a gofix with gishi. Cells are connected by further 120 diametral gid. Its vertex figure is a variation of qrid, in fact v3o5/3x or v3/2o5/2x (which degenerates to something what looks like a sissid plus an encasing v-ike, but diametral rectangles will there be in addition). Accordingly edges coincide by 5, all faces come in coincident pairs, and the gid also come in coincident pairs.

As abstract polytope gofix+gishi+120gid is isomorphic to fix+gahi+120id, thereby replacing pentagrams by pentagons resp. replacing gissid by doe, gike by ike and gid by id.

Incidence matrix according to Dynkin symbol

x3o5/2o3o5/3*a

. .   . .      | 120 |   60 |   60   60 |  12  30  20
---------------+-----+------+-----------+------------
x .   . .      |   2 | 3600 |    2    2 |   1   2   1
---------------+-----+------+-----------+------------
x3o   . .      |   3 |    3 | 2400    * |   1   1   0
x .   . o5/3*a |   5 |    5 |    * 1440 |   0   1   1
---------------+-----+------+-----------+------------
x3o5/2o .      ♦  12 |   30 |   20    0 | 120   *   *
x3o   . o5/3*a ♦  30 |   60 |   20   12 |   * 120   *
x .   o3o5/3*a ♦  20 |   30 |    0   12 |   *   * 120

x3o5/2o3/2o5/2*a

. .   .   .      | 120 |   60 |   60   60 |  12  30  20
-----------------+-----+------+-----------+------------
x .   .   .      |   2 | 3600 |    2    2 |   1   2   1
-----------------+-----+------+-----------+------------
x3o   .   .      |   3 |    3 | 2400    * |   1   1   0
x .   .   o5/2*a |   5 |    5 |    * 1440 |   0   1   1
-----------------+-----+------+-----------+------------
x3o5/2o   .      ♦  12 |   30 |   20    0 | 120   *   *
x3o   .   o5/2*a ♦  30 |   60 |   20   12 |   * 120   *
x .   o3/2o5/2*a ♦  20 |   30 |    0   12 |   *   * 120

x3o5/3o3o5/2*a

. .   . .      | 120 |   60 |   60   60 |  12  30  20
---------------+-----+------+-----------+------------
x .   . .      |   2 | 3600 |    2    2 |   1   2   1
---------------+-----+------+-----------+------------
x3o   . .      |   3 |    3 | 2400    * |   1   1   0
x .   . o5/2*a |   5 |    5 |    * 1440 |   0   1   1
---------------+-----+------+-----------+------------
x3o5/3o .      ♦  12 |   30 |   20    0 | 120   *   *
x3o   . o5/2*a ♦  30 |   60 |   20   12 |   * 120   *
x .   o3o5/2*a ♦  20 |   30 |    0   12 |   *   * 120

x3o5/3o3/2o5/3*a

. .   .   .      | 120 |   60 |   60   60 |  12  30  20
-----------------+-----+------+-----------+------------
x .   .   .      |   2 | 3600 |    2    2 |   1   2   1
-----------------+-----+------+-----------+------------
x3o   .   .      |   3 |    3 | 2400    * |   1   1   0
x .   .   o5/3*a |   5 |    5 |    * 1440 |   0   1   1
-----------------+-----+------+-----------+------------
x3o5/3o   .      ♦  12 |   30 |   20    0 | 120   *   *
x3o   .   o5/3*a ♦  30 |   60 |   20   12 |   * 120   *
x .   o3/2o5/3*a ♦  20 |   30 |    0   12 |   *   * 120

x3/2o5/2o3o5/2*a

.   .   . .      | 120 |   60 |   60   60 |  12  30  20
-----------------+-----+------+-----------+------------
x   .   . .      |   2 | 3600 |    2    2 |   1   2   1
-----------------+-----+------+-----------+------------
x3/2o   . .      |   3 |    3 | 2400    * |   1   1   0
x   .   . o5/2*a |   5 |    5 |    * 1440 |   0   1   1
-----------------+-----+------+-----------+------------
x3/2o5/2o .      ♦  12 |   30 |   20    0 | 120   *   *
x3/2o   . o5/2*a ♦  30 |   60 |   20   12 |   * 120   *
x   .   o3o5/2*a ♦  20 |   30 |    0   12 |   *   * 120

x3/2o5/2o3/2o5/3*a

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

x3/2o5/3o3o5/3*a

.   .   . .      | 120 |   60 |   60   60 |  12  30  20
-----------------+-----+------+-----------+------------
x   .   . .      |   2 | 3600 |    2    2 |   1   2   1
-----------------+-----+------+-----------+------------
x3/2o   . .      |   3 |    3 | 2400    * |   1   1   0
x   .   . o5/3*a |   5 |    5 |    * 1440 |   0   1   1
-----------------+-----+------+-----------+------------
x3/2o5/3o .      ♦  12 |   30 |   20    0 | 120   *   *
x3/2o   . o5/3*a ♦  30 |   60 |   20   12 |   * 120   *
x   .   o3o5/3*a ♦  20 |   30 |    0   12 |   *   * 120

x3/2o5/3o3/2o5/2*a

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