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

As abstract polytope 2gaghi is isomorphic to 2sishi, thereby replacing gad by sissid, resp. replacing 2gissid vertex figures by 2doe ones.

Incidence matrix according to Dynkin symbol

x5o5/2o3o5/3*b

. .   . .      | 120 ♦   20 |   60 |  12  12
---------------+-----+------+------+--------
x .   . .      |   2 | 1200 |    6 |   3   3
---------------+-----+------+------+--------
x5o   . .      |   5 |    5 | 1440 |   1   1
---------------+-----+------+------+--------
x5o5/2o .      ♦  12 |   30 |   12 | 120   *
x5o   . o5/3*b ♦  12 |   30 |   12 |   * 120

x5o5/2o3/2o5/2*b

. .   .   .      | 120 ♦   20 |   60 |  12  12
-----------------+-----+------+------+--------
x .   .   .      |   2 | 1200 |    6 |   3   3
-----------------+-----+------+------+--------
x5o   .   .      |   5 |    5 | 1440 |   1   1
-----------------+-----+------+------+--------
x5o5/2o   .      ♦  12 |   30 |   12 | 120   *
x5o   .   o5/2*b ♦  12 |   30 |   12 |   * 120

or
. .   .   .         | 120 ♦   20 |   60 |  24
--------------------+-----+------+------+----
x .   .   .         |   2 | 1200 |    6 |   6
--------------------+-----+------+------+----
x5o   .   .         |   5 |    5 | 1440 |   2
--------------------+-----+------+------+----
x5o5/2o   .       & ♦  12 |   30 |   12 | 240

x5o5/3o3/2o5/3*b

. .   .   .      | 120 ♦   20 |   60 |  12  12
-----------------+-----+------+------+--------
x .   .   .      |   2 | 1200 |    6 |   3   3
-----------------+-----+------+------+--------
x5o   .   .      |   5 |    5 | 1440 |   1   1
-----------------+-----+------+------+--------
x5o5/3o   .      ♦  12 |   30 |   12 | 120   *
x5o   .   o5/3*b ♦  12 |   30 |   12 |   * 120

or
. .   .   .         | 120 ♦   20 |   60 |  24
--------------------+-----+------+------+----
x .   .   .         |   2 | 1200 |    6 |   6
--------------------+-----+------+------+----
x5o   .   .         |   5 |    5 | 1440 |   2
--------------------+-----+------+------+----
x5o5/3o   .       & ♦  12 |   30 |   12 | 240

x5/4o5/2o3o5/3*b

.   .   . .      | 120 ♦   20 |   60 |  12  12
-----------------+-----+------+------+--------
x   .   . .      |   2 | 1200 |    6 |   3   3
-----------------+-----+------+------+--------
x5/4o   . .      |   5 |    5 | 1440 |   1   1
-----------------+-----+------+------+--------
x5/4o5/2o .      ♦  12 |   30 |   12 | 120   *
x5/4o   . o5/3*b ♦  12 |   30 |   12 |   * 120

x5/4o5/2o3/2o5/2*b

.   .   .   .      | 120 ♦   20 |   60 |  12  12
-------------------+-----+------+------+--------
x   .   .   .      |   2 | 1200 |    6 |   3   3
-------------------+-----+------+------+--------
x5/4o   .   .      |   5 |    5 | 1440 |   1   1
-------------------+-----+------+------+--------
x5/4o5/2o   .      ♦  12 |   30 |   12 | 120   *
x5/4o   .   o5/2*b ♦  12 |   30 |   12 |   * 120

or
.   .   .   .         | 120 ♦   20 |   60 |  24
----------------------+-----+------+------+----
x   .   .   .         |   2 | 1200 |    6 |   6
----------------------+-----+------+------+----
x5/4o   .   .         |   5 |    5 | 1440 |   2
----------------------+-----+------+------+----
x5/4o5/2o   .       & ♦  12 |   30 |   12 | 240

x5/4o5/3o3/2o5/3*b

.   .   .   .      | 120 ♦   20 |   60 |  12  12
-------------------+-----+------+------+--------
x   .   .   .      |   2 | 1200 |    6 |   3   3
-------------------+-----+------+------+--------
x5/4o   .   .      |   5 |    5 | 1440 |   1   1
-------------------+-----+------+------+--------
x5/4o5/3o   .      ♦  12 |   30 |   12 | 120   *
x5/4o   .   o5/3*b ♦  12 |   30 |   12 |   * 120

or
.   .   .   .         | 120 ♦   20 |   60 |  24
----------------------+-----+------+------+----
x   .   .   .         |   2 | 1200 |    6 |   6
----------------------+-----+------+------+----
x5/4o   .   .         |   5 |    5 | 1440 |   2
----------------------+-----+------+------+----
x5/4o5/3o   .       & ♦  12 |   30 |   12 | 240