Acronym ...
Name 2gashi (?)
Circumradius (sqrt(5)-1)/2 = 0.618034
Inradius (3-sqrt(5))/4 = 0.190983
General of army ex
Colonel of regiment gishi
Confer
non-Grünbaumian master:
gashi  
Grünbaumian relatives:
gax+gashi+120gid  

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

As abstract polytope 2gashi is isomorphic to 2gohi, thereby replacing pentagrams by pentagons, resp. replacing sissid by gad, resp. replacing 2gad vertex figures by 2sissid ones.


Incidence matrix according to Dynkin symbol

x5/2o5o5o5/4*b

.   . . .      | 120   12 |   60 |  12  12
---------------+-----+-----+------+--------
x   . . .      |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/2o . .      |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/2o5o .        12 |  30 |   12 | 120   *
x5/2o . o5/4*b   12 |  30 |   12 |   * 120

x5/2o5o5/4o5*b

.   . .   .    | 120   12 |   60 |  12  12
---------------+-----+-----+------+--------
x   . .   .    |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/2o .   .    |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/2o5o   .      12 |  30 |   12 | 120   *
x5/2o .   o5*b   12 |  30 |   12 |   * 120
or
.   . .   .       | 120   12 |   60 |  24
------------------+-----+-----+------+----
x   . .   .       |   2 | 720 |   10 |  10
------------------+-----+-----+------+----
x5/2o .   .       |   5 |   5 | 1440 |   2
------------------+-----+-----+------+----
x5/2o5o   .     &   12 |  30 |   12 | 240

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

.   .   .   .      | 120   12 |   60 |  12  12
-------------------+-----+-----+------+--------
x   .   .   .      |   2 | 720 |   10 |   5   5
-------------------+-----+-----+------+--------
x5/2o   .   .      |   5 |   5 | 1440 |   1   1
-------------------+-----+-----+------+--------
x5/2o5/4o   .        12 |  30 |   12 | 120   *
x5/2o   .   o5/4*b   12 |  30 |   12 |   * 120
or
.   .   .   .         | 120   12 |   60 |  24
----------------------+-----+-----+------+----
x   .   .   .         |   2 | 720 |   10 |  10
----------------------+-----+-----+------+----
x5/2o   .   .         |   5 |   5 | 1440 |   2
----------------------+-----+-----+------+----
x5/2o5/4o   .       &   12 |  30 |   12 | 240

x5/3o5o5o5/4*b

.   . . .      | 120   12 |   60 |  12  12
---------------+-----+-----+------+--------
x   . . .      |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/3o . .      |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/3o5o .        12 |  30 |   12 | 120   *
x5/3o . o5/4*b   12 |  30 |   12 |   * 120

x5/3o5o5/4o5*b

.   . .   .    | 120   12 |   60 |  12  12
---------------+-----+-----+------+--------
x   . .   .    |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/3o .   .    |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/3o5o   .      12 |  30 |   12 | 120   *
x5/3o .   o5*b   12 |  30 |   12 |   * 120
or
.   . .   .       | 120   12 |   60 |  24
------------------+-----+-----+------+----
x   . .   .       |   2 | 720 |   10 |  10
------------------+-----+-----+------+----
x5/3o .   .       |   5 |   5 | 1440 |   2
------------------+-----+-----+------+----
x5/3o5o   .     &   12 |  30 |   12 | 240

x5/3o5/4o5/4o5/4*b

.   .   .   .      | 120   12 |   60 |  12  12
-------------------+-----+-----+------+--------
x   .   .   .      |   2 | 720 |   10 |   5   5
-------------------+-----+-----+------+--------
x5/3o   .   .      |   5 |   5 | 1440 |   1   1
-------------------+-----+-----+------+--------
x5/3o5/4o   .        12 |  30 |   12 | 120   *
x5/3o   .   o5/4*b   12 |  30 |   12 |   * 120
or
.   .   .   .         | 120   12 |   60 |  24
----------------------+-----+-----+------+----
x   .   .   .         |   2 | 720 |   10 |  10
----------------------+-----+-----+------+----
x5/3o   .   .         |   5 |   5 | 1440 |   2
----------------------+-----+-----+------+----
x5/3o5/4o   .       &   12 |  30 |   12 | 240

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