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

As abstract polytope 2gax is isomorphic to 2ex, thereby replacing {10/4} edge figures by {10/2} ones resp. replacing 2gike vertex figures by 2ike ones.

Incidence matrix according to Dynkin symbol

x3o3o5o3/2*b

. . . .      | 120 ♦  12 |   60 |  20  20
-------------+-----+-----+------+--------
x . . .      |   2 | 720 |   10 |   5   5
-------------+-----+-----+------+--------
x3o . .      |   3 |   3 | 2400 |   1   1
-------------+-----+-----+------+--------
x3o3o .      ♦   4 |   6 |    4 | 600   *
x3o . o3/2*b ♦   4 |   6 |    4 |   * 600

x3o3o5/4o3*b

. . .   .    | 120 ♦  12 |   60 |  20  20
-------------+-----+-----+------+--------
x . .   .    |   2 | 720 |   10 |   5   5
-------------+-----+-----+------+--------
x3o .   .    |   3 |   3 | 2400 |   1   1
-------------+-----+-----+------+--------
x3o3o   .    ♦   4 |   6 |    4 | 600   *
x3o .   o3*b ♦   4 |   6 |    4 |   * 600

or
. . .   .       | 120 ♦  12 |   60 |   40
----------------+-----+-----+------+-----
x . .   .       |   2 | 720 |   10 |   10
----------------+-----+-----+------+-----
x3o .   .       |   3 |   3 | 2400 |    2
----------------+-----+-----+------+-----
x3o3o   .     & ♦   4 |   6 |    4 | 1200

x3o3/2o5/4o3/2*b

. .   .   .      | 120 ♦  12 |   60 |  20  20
-----------------+-----+-----+------+--------
x .   .   .      |   2 | 720 |   10 |   5   5
-----------------+-----+-----+------+--------
x3o   .   .      |   3 |   3 | 2400 |   1   1
-----------------+-----+-----+------+--------
x3o3/2o   .      ♦   4 |   6 |    4 | 600   *
x3o   .   o3/2*b ♦   4 |   6 |    4 |   * 600

or
. .   .   .         | 120 ♦  12 |   60 |   40
--------------------+-----+-----+------+-----
x .   .   .         |   2 | 720 |   10 |   10
--------------------+-----+-----+------+-----
x3o   .   .         |   3 |   3 | 2400 |    2
--------------------+-----+-----+------+-----
x3o3/2o   .       & ♦   4 |   6 |    4 | 1200

x3/2o3o5o3/2*b

.   . . .      | 120 ♦  12 |   60 |  20  20
---------------+-----+-----+------+--------
x   . . .      |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x3/2o . .      |   3 |   3 | 2400 |   1   1
---------------+-----+-----+------+--------
x3/2o3o .      ♦   4 |   6 |    4 | 600   *
x3/2o . o3/2*b ♦   4 |   6 |    4 |   * 600

x3/2o3o5/4o3*b

.   . .   .    | 120 ♦  12 |   60 |  20  20
---------------+-----+-----+------+--------
x   . .   .    |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x3/2o .   .    |   3 |   3 | 2400 |   1   1
---------------+-----+-----+------+--------
x3/2o3o   .    ♦   4 |   6 |    4 | 600   *
x3/2o .   o3*b ♦   4 |   6 |    4 |   * 600

or
.   . .   .       | 120 ♦  12 |   60 |   40
------------------+-----+-----+------+-----
x   . .   .       |   2 | 720 |   10 |   10
------------------+-----+-----+------+-----
x3/2o .   .       |   3 |   3 | 2400 |    2
------------------+-----+-----+------+-----
x3/2o3o   .     & ♦   4 |   6 |    4 | 1200

x3/2o3/2o5/4o3/2*b

.   .   .   .      | 120 ♦  12 |   60 |  20  20
-------------------+-----+-----+------+--------
x   .   .   .      |   2 | 720 |   10 |   5   5
-------------------+-----+-----+------+--------
x3/2o   .   .      |   3 |   3 | 2400 |   1   1
-------------------+-----+-----+------+--------
x3/2o3/2o   .      ♦   4 |   6 |    4 | 600   *
x3/2o   .   o3/2*b ♦   4 |   6 |    4 |   * 600

or
.   .   .   .         | 120 ♦  12 |   60 |   40
----------------------+-----+-----+------+-----
x   .   .   .         |   2 | 720 |   10 |   10
----------------------+-----+-----+------+-----
x3/2o   .   .         |   3 |   3 | 2400 |    2
----------------------+-----+-----+------+-----
x3/2o3/2o   .       & ♦   4 |   6 |    4 | 1200