Acronym ...
Name sishi+gaghi+idhi (?)
Circumradius 1
General of army ex
Colonel of regiment sishi
Confer gaghi   gaghi+idhi   idhi   sishi   sishi+gaghi+120did   sishi+idhi   sishi+paphicki+gridaphi   2sishi   2sishi+2paphicki  

Looks like a compound of a sishi, gaghi, and idhi. Its vertex figure is v3/2f5/2o5*a, which in turn looks like the compound of the vertex figures of these 3 components. Edges coincide by 3 and faces come in coincident pairs.

As abstract polytope sishi+gaghi+idhi is autoomorph, thereby interchanging pentagrams and pentagons resp. sissid and gad.


Incidence matrix according to Dynkin symbol

o5x5/3o5o5/3*a3*c

. .   . .         | 120 |   60 |   60   60 |  20  12  12
------------------+-----+------+-----------+------------
. x   . .         |   2 | 3600 |    2    2 |   2   1   1
------------------+-----+------+-----------+------------
o5x   . .         |   5 |    5 | 1440    * |   1   1   0
. x5/3o .         |   5 |    5 |    * 1440 |   1   0   1
------------------+-----+------+-----------+------------
o5x5/3o .   *a3*c   20 |   60 |   12   12 | 120   *   *
o5x   . o5/3*a      12 |   30 |   12    0 |   * 120   *
. x5/3o5o           12 |   30 |    0   12 |   *   * 120

o5x5/2o5o5/2*a3/2*c

. .   . .           | 120 |   60 |   60   60 |  20  12  12
--------------------+-----+------+-----------+------------
. x   . .           |   2 | 3600 |    2    2 |   2   1   1
--------------------+-----+------+-----------+------------
o5x   . .           |   5 |    5 | 1440    * |   1   1   0
. x5/2o .           |   5 |    5 |    * 1440 |   1   0   1
--------------------+-----+------+-----------+------------
o5x5/2o .   *a3/2*c   20 |   60 |   12   12 | 120   *   *
o5x   . o5/2*a        12 |   30 |   12    0 |   * 120   *
. x5/2o5o             12 |   30 |    0   12 |   *   * 120

o5x5/3o5/4o5/2*a3*c

. .   .   .         | 120 |   60 |   60   60 |  20  12  12
--------------------+-----+------+-----------+------------
. x   .   .         |   2 | 3600 |    2    2 |   2   1   1
--------------------+-----+------+-----------+------------
o5x   .   .         |   5 |    5 | 1440    * |   1   1   0
. x5/3o   .         |   5 |    5 |    * 1440 |   1   0   1
--------------------+-----+------+-----------+------------
o5x5/3o   .   *a3*c   20 |   60 |   12   12 | 120   *   *
o5x   .   o5/2*a      12 |   30 |   12    0 |   * 120   *
. x5/3o5/4o           12 |   30 |    0   12 |   *   * 120

o5x5/2o5/4o5/3*a3/2*c

. .   .   .           | 120 |   60 |   60   60 |  20  12  12
----------------------+-----+------+-----------+------------
. x   .   .           |   2 | 3600 |    2    2 |   2   1   1
----------------------+-----+------+-----------+------------
o5x   .   .           |   5 |    5 | 1440    * |   1   1   0
. x5/2o   .           |   5 |    5 |    * 1440 |   1   0   1
----------------------+-----+------+-----------+------------
o5x5/2o   .   *a3/2*c   20 |   60 |   12   12 | 120   *   *
o5x   .   o5/3*a        12 |   30 |   12    0 |   * 120   *
. x5/2o5/4o             12 |   30 |    0   12 |   *   * 120

o5/4x5/2o5o5/3*a3*c

.   .   . .         | 120 |   60 |   60   60 |  20  12  12
--------------------+-----+------+-----------+------------
.   x   . .         |   2 | 3600 |    2    2 |   2   1   1
--------------------+-----+------+-----------+------------
o5/4x   . .         |   5 |    5 | 1440    * |   1   1   0
.   x5/2o .         |   5 |    5 |    * 1440 |   1   0   1
--------------------+-----+------+-----------+------------
o5/4x5/2o .   *a3*c   20 |   60 |   12   12 | 120   *   *
o5/4x   . o5/3*a      12 |   30 |   12    0 |   * 120   *
.   x5/2o5o           12 |   30 |    0   12 |   *   * 120

o5/4x5/3o5o5/2*a3/2*c

.   .   . .           | 120 |   60 |   60   60 |  20  12  12
----------------------+-----+------+-----------+------------
.   x   . .           |   2 | 3600 |    2    2 |   2   1   1
----------------------+-----+------+-----------+------------
o5/4x   . .           |   5 |    5 | 1440    * |   1   1   0
.   x5/3o .           |   5 |    5 |    * 1440 |   1   0   1
----------------------+-----+------+-----------+------------
o5/4x5/3o .   *a3/2*c   20 |   60 |   12   12 | 120   *   *
o5/4x   . o5/2*a        12 |   30 |   12    0 |   * 120   *
.   x5/3o5o             12 |   30 |    0   12 |   *   * 120

o5/4x5/2o5/4o5/2*a3*c

.   .   .   .         | 120 |   60 |   60   60 |  20  12  12
----------------------+-----+------+-----------+------------
.   x   .   .         |   2 | 3600 |    2    2 |   2   1   1
----------------------+-----+------+-----------+------------
o5/4x   .   .         |   5 |    5 | 1440    * |   1   1   0
.   x5/2o   .         |   5 |    5 |    * 1440 |   1   0   1
----------------------+-----+------+-----------+------------
o5/4x5/2o   .   *a3*c   20 |   60 |   12   12 | 120   *   *
o5/4x   .   o5/2*a      12 |   30 |   12    0 |   * 120   *
.   x5/2o5/4o           12 |   30 |    0   12 |   *   * 120

o5/4x5/3o5/4o5/3*a3/2*c

.   .   .   .           | 120 |   60 |   60   60 |  20  12  12
------------------------+-----+------+-----------+------------
.   x   .   .           |   2 | 3600 |    2    2 |   2   1   1
------------------------+-----+------+-----------+------------
o5/4x   .   .           |   5 |    5 | 1440    * |   1   1   0
.   x5/3o   .           |   5 |    5 |    * 1440 |   1   0   1
------------------------+-----+------+-----------+------------
o5/4x5/3o   .   *a3/2*c   20 |   60 |   12   12 | 120   *   *
o5/4x   .   o5/3*a        12 |   30 |   12    0 |   * 120   *
.   x5/3o5/4o             12 |   30 |    0   12 |   *   * 120

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