Looks like a compound of dittady and dox. Its vertex figure is the already degenerate cadditradid. Accordingly the edges coincide by 3. Also the 2 classes of triangles coincide one by one.

As abstract polytope dittady+dox is automorph, thereby interchanging gike and ike.

Incidence matrix according to Dynkin symbol

x3o5o5/2o3/2*a

. . .   .      | 120 ♦   60 |   60   60 |  12  30  12
---------------+-----+------+-----------+------------
x . .   .      |   2 | 3600 |    2    2 |   1   2   1
---------------+-----+------+-----------+------------
x3o .   .      |   3 |    3 | 2400    * |   1   1   0
x . .   o3/2*a |   3 |    3 |    * 2400 |   0   1   1
---------------+-----+------+-----------+------------
x3o5o   .      ♦  12 |   30 |   20    0 | 120   *   *
x3o .   o3/2*a ♦   6 |   12 |    4    4 |   * 600   *
x . o5/2o3/2*a ♦  12 |   30 |    0   20 |   *   * 120

x3o5o5/3o3*a

. . .   .    | 120 ♦   60 |   60   60 |  12  30  12
-------------+-----+------+-----------+------------
x . .   .    |   2 | 3600 |    2    2 |   1   2   1
-------------+-----+------+-----------+------------
x3o .   .    |   3 |    3 | 2400    * |   1   1   0
x . .   o3*a |   3 |    3 |    * 2400 |   0   1   1
-------------+-----+------+-----------+------------
x3o5o   .    ♦  12 |   30 |   20    0 | 120   *   *
x3o .   o3*a ♦   6 |   12 |    4    4 |   * 600   *
x . o5/3o3*a ♦  12 |   30 |    0   20 |   *   * 120

x3o5/4o5/2o3*a

. .   .   .    | 120 ♦   60 |   60   60 |  12  30  12
---------------+-----+------+-----------+------------
x .   .   .    |   2 | 3600 |    2    2 |   1   2   1
---------------+-----+------+-----------+------------
x3o   .   .    |   3 |    3 | 2400    * |   1   1   0
x .   .   o3*a |   3 |    3 |    * 2400 |   0   1   1
---------------+-----+------+-----------+------------
x3o5/4o   .    ♦  12 |   30 |   20    0 | 120   *   *
x3o   .   o3*a ♦   6 |   12 |    4    4 |   * 600   *
x .   o5/2o3*a ♦  12 |   30 |    0   20 |   *   * 120

x3/2o5o5/2o3*a

.   . .   .    | 120 ♦   60 |   60   60 |  12  30  12
---------------+-----+------+-----------+------------
x   . .   .    |   2 | 3600 |    2    2 |   1   2   1
---------------+-----+------+-----------+------------
x3/2o .   .    |   3 |    3 | 2400    * |   1   1   0
x   . .   o3*a |   3 |    3 |    * 2400 |   0   1   1
---------------+-----+------+-----------+------------
x3/2o5o   .    ♦  12 |   30 |   20    0 | 120   *   *
x3/2o .   o3*a ♦   6 |   12 |    4    4 |   * 600   *
x   . o5/2o3*a ♦  12 |   30 |    0   20 |   *   * 120

x3o5/4o5/3o3/2*a

. .   .   .      | 120 ♦   60 |   60   60 |  12  30  12
-----------------+-----+------+-----------+------------
x .   .   .      |   2 | 3600 |    2    2 |   1   2   1
-----------------+-----+------+-----------+------------
x3o   .   .      |   3 |    3 | 2400    * |   1   1   0
x .   .   o3/2*a |   3 |    3 |    * 2400 |   0   1   1
-----------------+-----+------+-----------+------------
x3o5/4o   .      ♦  12 |   30 |   20    0 | 120   *   *
x3o   .   o3/2*a ♦   6 |   12 |    4    4 |   * 600   *
x .   o5/3o3/2*a ♦  12 |   30 |    0   20 |   *   * 120

x3/2o5o5/3o3/2*a

.   . .   .      | 120 ♦   60 |   60   60 |  12  30  12
-----------------+-----+------+-----------+------------
x   . .   .      |   2 | 3600 |    2    2 |   1   2   1
-----------------+-----+------+-----------+------------
x3/2o .   .      |   3 |    3 | 2400    * |   1   1   0
x   . .   o3/2*a |   3 |    3 |    * 2400 |   0   1   1
-----------------+-----+------+-----------+------------
x3/2o5o   .      ♦  12 |   30 |   20    0 | 120   *   *
x3/2o .   o3/2*a ♦   6 |   12 |    4    4 |   * 600   *
x   . o5/3o3/2*a ♦  12 |   30 |    0   20 |   *   * 120

x3/2o5/4o5/2o3/2*a

.   .   .   .      | 120 ♦   60 |   60   60 |  12  30  12
-------------------+-----+------+-----------+------------
x   .   .   .      |   2 | 3600 |    2    2 |   1   2   1
-------------------+-----+------+-----------+------------
x3/2o   .   .      |   3 |    3 | 2400    * |   1   1   0
x   .   .   o3/2*a |   3 |    3 |    * 2400 |   0   1   1
-------------------+-----+------+-----------+------------
x3/2o5/4o   .      ♦  12 |   30 |   20    0 | 120   *   *
x3/2o   .   o3/2*a ♦   6 |   12 |    4    4 |   * 600   *
x   .   o5/2o3/2*a ♦  12 |   30 |    0   20 |   *   * 120

x3/2o5/4o5/3o3*a

.   .   .   .    | 120 ♦   60 |   60   60 |  12  30  12
-----------------+-----+------+-----------+------------
x   .   .   .    |   2 | 3600 |    2    2 |   1   2   1
-----------------+-----+------+-----------+------------
x3/2o   .   .    |   3 |    3 | 2400    * |   1   1   0
x   .   .   o3*a |   3 |    3 |    * 2400 |   0   1   1
-----------------+-----+------+-----------+------------
x3/2o5/4o   .    ♦  12 |   30 |   20    0 | 120   *   *
x3/2o   .   o3*a ♦   6 |   12 |    4    4 |   * 600   *
x   .   o5/3o3*a ♦  12 |   30 |    0   20 |   *   * 120