Acronym ...
Name gishi+gashi (?)
Circumradius (sqrt(5)-1)/2 = 0.618034
General of army ex
Colonel of regiment gishi
Confer gishi   2gishi   gashi   2gashi   gax+gashi+120gid  

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

As abstract polytope gishi+gashi is isomorphic to gahi+gohi, thereby just scaling the edge figure, a complete pentagon, resp. replacing gissid by doe, sissid by gad, and replacing cid vertex figures by gacid ones.

Just as cid itself (with vertices being identified) comes in 2 flavors, type A) as in o3/2x5o5*a with vertex figure [(3/2,5)5] or type B) as in o5/3o3x5*a with vertex figure [(3,5)5]/3, accordingly either one can be used as vertex figure here too. Thus gishi+gashi comes alike in 2 corresponding flavors (types being marked accordingly).


Incidence matrix according to Dynkin symbol

x5/2o3o5o5/4*b (type A)

.   . . .      | 120   12 |   60 |  20  12
---------------+-----+-----+------+--------
x   . . .      |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/2o . .      |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/2o3o .        20 |  30 |   12 | 120   *
x5/2o . o5/4*b   12 |  30 |   12 |   * 120

x5/2o3o5/4o5*b (type A)

.   . .   .    | 120   12 |   60 |  20  12
---------------+-----+-----+------+--------
x   . .   .    |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/2o .   .    |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/2o3o   .      20 |  30 |   12 | 120   *
x5/2o .   o5*b   12 |  30 |   12 |   * 120

x5/2o3/2o5o5*b (type A)

.   .   . .    | 120   12 |   60 |  20  12
---------------+-----+-----+------+--------
x   .   . .    |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/2o   . .    |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/2o3/2o .      20 |  30 |   12 | 120   *
x5/2o   . o5*b   12 |  30 |   12 |   * 120

x5/2o3/2o5/4o5/4*b (type A)

.   .   .   .      | 120   12 |   60 |  20  12
-------------------+-----+-----+------+--------
x   .   .   .      |   2 | 720 |   10 |   5   5
-------------------+-----+-----+------+--------
x5/2o   .   .      |   5 |   5 | 1440 |   1   1
-------------------+-----+-----+------+--------
x5/2o3/2o   .        20 |  30 |   12 | 120   *
x5/2o   .   o5/4*b   12 |  30 |   12 |   * 120

x5/3o3o5o5/4*b (type A)

.   . . .      | 120   12 |   60 |  20  12
---------------+-----+-----+------+--------
x   . . .      |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/3o . .      |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/3o3o .        20 |  30 |   12 | 120   *
x5/3o . o5/4*b   12 |  30 |   12 |   * 120

x5/3o3o5/4o5*b (type A)

.   . .   .    | 120   12 |   60 |  20  12
---------------+-----+-----+------+--------
x   . .   .    |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/3o .   .    |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/3o3o   .      20 |  30 |   12 | 120   *
x5/3o .   o5*b   12 |  30 |   12 |   * 120

x5/3o3/2o5o5*b (type A)

.   .   . .    | 120   12 |   60 |  20  12
---------------+-----+-----+------+--------
x   .   . .    |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/3o   . .    |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/3o3/2o .      20 |  30 |   12 | 120   *
x5/3o   . o5*b   12 |  30 |   12 |   * 120

x5/3o3/2o5/4o5/4*b (type A)

.   .   .   .      | 120   12 |   60 |  20  12
-------------------+-----+-----+------+--------
x   .   .   .      |   2 | 720 |   10 |   5   5
-------------------+-----+-----+------+--------
x5/3o   .   .      |   5 |   5 | 1440 |   1   1
-------------------+-----+-----+------+--------
x5/3o3/2o   .        20 |  30 |   12 | 120   *
x5/3o   .   o5/4*b   12 |  30 |   12 |   * 120

x5/2o3o5/2o5/4*b (type B)

.   . .   .      | 120   12 |   60 |  20  12
-----------------+-----+-----+------+--------
x   . .   .      |   2 | 720 |   10 |   5   5
-----------------+-----+-----+------+--------
x5/2o .   .      |   5 |   5 | 1440 |   1   1
-----------------+-----+-----+------+--------
x5/2o3o   .        20 |  30 |   12 | 120   *
x5/2o .   o5/4*b   12 |  30 |   12 |   * 120

x5/2o3o5/3o5*b (type B)

.   . .   .    | 120   12 |   60 |  20  12
---------------+-----+-----+------+--------
x   . .   .    |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/2o .   .    |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/2o3o   .      20 |  30 |   12 | 120   *
x5/2o .   o5*b   12 |  30 |   12 |   * 120

x5/2o3/2o5/2o5*b (type B)

.   .   .   .    | 120   12 |   60 |  20  12
-----------------+-----+-----+------+--------
x   .   .   .    |   2 | 720 |   10 |   5   5
-----------------+-----+-----+------+--------
x5/2o   .   .    |   5 |   5 | 1440 |   1   1
-----------------+-----+-----+------+--------
x5/2o3/2o   .      20 |  30 |   12 | 120   *
x5/2o   .   o5*b   12 |  30 |   12 |   * 120

x5/2o3/2o5/3o5/4*b (type B)

.   .   .   .      | 120   12 |   60 |  20  12
-------------------+-----+-----+------+--------
x   .   .   .      |   2 | 720 |   10 |   5   5
-------------------+-----+-----+------+--------
x5/2o   .   .      |   5 |   5 | 1440 |   1   1
-------------------+-----+-----+------+--------
x5/2o3/2o   .        20 |  30 |   12 | 120   *
x5/2o   .   o5/4*b   12 |  30 |   12 |   * 120

x5/3o3o5/2o5/4*b (type B)

.   . .   .      | 120   12 |   60 |  20  12
-----------------+-----+-----+------+--------
x   . .   .      |   2 | 720 |   10 |   5   5
-----------------+-----+-----+------+--------
x5/3o .   .      |   5 |   5 | 1440 |   1   1
-----------------+-----+-----+------+--------
x5/3o3o   .        20 |  30 |   12 | 120   *
x5/3o .   o5/4*b   12 |  30 |   12 |   * 120

x5/3o3o5/3o5*b (type B)

.   . .   .    | 120   12 |   60 |  20  12
---------------+-----+-----+------+--------
x   . .   .    |   2 | 720 |   10 |   5   5
---------------+-----+-----+------+--------
x5/3o .   .    |   5 |   5 | 1440 |   1   1
---------------+-----+-----+------+--------
x5/3o3o   .      20 |  30 |   12 | 120   *
x5/3o .   o5*b   12 |  30 |   12 |   * 120

x5/3o3/2o5/2o5*b (type B)

.   .   .   .    | 120   12 |   60 |  20  12
-----------------+-----+-----+------+--------
x   .   .   .    |   2 | 720 |   10 |   5   5
-----------------+-----+-----+------+--------
x5/3o   .   .    |   5 |   5 | 1440 |   1   1
-----------------+-----+-----+------+--------
x5/3o3/2o   .      20 |  30 |   12 | 120   *
x5/3o   .   o5*b   12 |  30 |   12 |   * 120

x5/3o3/2o5/3o5/4*b (type B)

.   .   .   .      | 120   12 |   60 |  20  12
-------------------+-----+-----+------+--------
x   .   .   .      |   2 | 720 |   10 |   5   5
-------------------+-----+-----+------+--------
x5/3o   .   .      |   5 |   5 | 1440 |   1   1
-------------------+-----+-----+------+--------
x5/3o3/2o   .        20 |  30 |   12 | 120   *
x5/3o   .   o5/4*b   12 |  30 |   12 |   * 120

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