Acronym ...
Name 2sishi (?)
Circumradius 1
Inradius (1+sqrt(5))/4 = 0.809017
General of army ex
Colonel of regiment sishi
Confer
non-Grünbaumian master:
sishi  
Grünbaumian relatives:
sishi+gaghi+120did   sishi+paphicki+gridaphi   2sishi+2paphicki  

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

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


Incidence matrix according to Dynkin symbol

x5/2o5o3o5/4*b

.   . . .      | 120    20 |   60 |  12  12
---------------+-----+------+------+--------
x   . . .      |   2 | 1200 |    6 |   3   3
---------------+-----+------+------+--------
x5/2o . .      |   5 |    5 | 1440 |   1   1
---------------+-----+------+------+--------
x5/2o5o .        12 |   30 |   12 | 120   *
x5/2o . o5/4*b   12 |   30 |   12 |   * 120

x5/2o5o3/2o5*b

.   . .   .    | 120    20 |   60 |  12  12
---------------+-----+------+------+--------
x   . .   .    |   2 | 1200 |    6 |   3   3
---------------+-----+------+------+--------
x5/2o .   .    |   5 |    5 | 1440 |   1   1
---------------+-----+------+------+--------
x5/2o5o   .      12 |   30 |   12 | 120   *
x5/2o .   o5*b   12 |   30 |   12 |   * 120
or
.   . .   .       | 120    20 |   60 |  24
------------------+-----+------+------+----
x   . .   .       |   2 | 1200 |    6 |   6
------------------+-----+------+------+----
x5/2o .   .       |   5 |    5 | 1440 |   2
------------------+-----+------+------+----
x5/2o5o   .     &   12 |   30 |   12 | 240

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

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

x5/3o5o3o5/4*b

.   . . .      | 120    20 |   60 |  12  12
---------------+-----+------+------+--------
x   . . .      |   2 | 1200 |    6 |   3   3
---------------+-----+------+------+--------
x5/3o . .      |   5 |    5 | 1440 |   1   1
---------------+-----+------+------+--------
x5/3o5o .        12 |   30 |   12 | 120   *
x5/3o . o5/4*b   12 |   30 |   12 |   * 120

x5/3o5o3/2o5*b

.   . .   .    | 120    20 |   60 |  12  12
---------------+-----+------+------+--------
x   . .   .    |   2 | 1200 |    6 |   3   3
---------------+-----+------+------+--------
x5/3o .   .    |   5 |    5 | 1440 |   1   1
---------------+-----+------+------+--------
x5/3o5o   .      12 |   30 |   12 | 120   *
x5/3o .   o5*b   12 |   30 |   12 |   * 120
or
.   . .   .       | 120    20 |   60 |  24
------------------+-----+------+------+----
x   . .   .       |   2 | 1200 |    6 |   6
------------------+-----+------+------+----
x5/3o .   .       |   5 |    5 | 1440 |   2
------------------+-----+------+------+----
x5/3o5o   .     &   12 |   30 |   12 | 240

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

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

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