Acronym ...
Name 2gogishi (?)
Circumradius sqrt[7-3 sqrt(5)] = 0.540182
Inradius (7-3 sqrt(5))/4 = 0.072949
General of army hi
Colonel of regiment gogishi
Confer
non-Grünbaumian master:
gogishi  

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

As abstract polytope 2gogishi is isomorphic to 2hi, thereby replacing pentagrams by pentagons resp. replacing gissid by doe.


Incidence matrix according to Dynkin symbol

x5/2o3o3o3/2*b

.   . . .      | 600     4 |   12 |   4   4
-------------+-----+------+------+--------
x   . . .      |   2 | 1200 |    6 |   3   3
-------------+-----+------+------+--------
x5/2o . .      |   5 |    5 | 1440 |   1   1
-------------+-----+------+------+--------
x5/2o3o .        20 |   30 |   12 | 120   *
x5/2o . o3/2*b   20 |   30 |   12 |   * 120

x5/2o3o3/2o3*b

.   . .   .    | 600     4 |   12 |   4   4
-------------+-----+------+------+--------
x   . .   .    |   2 | 1200 |    6 |   3   3
-------------+-----+------+------+--------
x5/2o .   .    |   5 |    5 | 1440 |   1   1
-------------+-----+------+------+--------
x5/2o3o   .      20 |   30 |   12 | 120   *
x5/2o .   o3*b   20 |   30 |   12 |   * 120
or
.   . .   .       | 600     4 |   12 |   8
----------------+-----+------+------+----
x   . .   .       |   2 | 1200 |    6 |   6
----------------+-----+------+------+----
x5/2o .   .       |   5 |    5 | 1440 |   2
----------------+-----+------+------+----
x5/2o3o   .     &   20 |   30 |   12 | 240

x5/2o3/2o3/2o3/2*b

.   .   .   .      | 600     4 |   12 |   4   4
-----------------+-----+------+------+--------
x   .   .   .      |   2 | 1200 |    6 |   3   3
-----------------+-----+------+------+--------
x5/2o   .   .      |   5 |    5 | 1440 |   1   1
-----------------+-----+------+------+--------
x5/2o3/2o   .        20 |   30 |   12 | 120   *
x5/2o   .   o3/2*b   20 |   30 |   12 |   * 120
or
.   .   .   .         | 600     4 |   12 |   8
--------------------+-----+------+------+----
x   .   .   .         |   2 | 1200 |    6 |   6
--------------------+-----+------+------+----
x5/2o   .   .         |   5 |    5 | 1440 |   2
--------------------+-----+------+------+----
x5/2o3/2o   .       &   20 |   30 |   12 | 240

x5/3o3o3o3/2*b

.   . . .      | 600     4 |   12 |   4   4
---------------+-----+------+------+--------
x   . . .      |   2 | 1200 |    6 |   3   3
---------------+-----+------+------+--------
x5/3o . .      |   5 |    5 | 1440 |   1   1
---------------+-----+------+------+--------
x5/3o3o .        20 |   30 |   12 | 120   *
x5/3o . o3/2*b   20 |   30 |   12 |   * 120

x5/3o3o3/2o3*b

.   . .   .    | 600     4 |   12 |   4   4
---------------+-----+------+------+--------
x   . .   .    |   2 | 1200 |    6 |   3   3
---------------+-----+------+------+--------
x5/3o .   .    |   5 |    5 | 1440 |   1   1
---------------+-----+------+------+--------
x5/3o3o   .      20 |   30 |   12 | 120   *
x5/3o .   o3*b   20 |   30 |   12 |   * 120
or
.   . .   .       | 600     4 |   12 |   8
------------------+-----+------+------+----
x   . .   .       |   2 | 1200 |    6 |   6
------------------+-----+------+------+----
x5/3o .   .       |   5 |    5 | 1440 |   2
------------------+-----+------+------+----
x5/3o3o   .     &   20 |   30 |   12 | 240

x5/3o3/2o3/2o3/2*b

.   .   .   .      | 600     4 |   12 |   4   4
-------------------+-----+------+------+--------
x   .   .   .      |   2 | 1200 |    6 |   3   3
-------------------+-----+------+------+--------
x5/3o   .   .      |   5 |    5 | 1440 |   1   1
-------------------+-----+------+------+--------
x5/3o3/2o   .        20 |   30 |   12 | 120   *
x5/3o   .   o3/2*b   20 |   30 |   12 |   * 120
or
.   .   .   .         | 600     4 |   12 |   8
----------------------+-----+------+------+----
x   .   .   .         |   2 | 1200 |    6 |   6
----------------------+-----+------+------+----
x5/3o   .   .         |   5 |    5 | 1440 |   2
----------------------+-----+------+------+----
x5/3o3/2o   .       &   20 |   30 |   12 | 240

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