Acronym ...
Name 2sishi+2paphicki (?)
Circumradius 1
General of army ex
Colonel of regiment sishi
Confer
non-Grünbaumian masters:
sishi   paphicki  
Grünbaumian relatives:
sishi+gaghi+120did   sishi+paphicki+gridaphi   2sishi  

2sishi+2paphicki (?) clearly is an edge-faceting of the small stellated hecatonicosachoron (sishi). Thus the vertices coincide by 12 each, further edges coincide by 6, pentagrams by 4, and all other elements by pairs.

As abstract polytope 2sishi+2paphicki is isomorphic to 2gaghi+2paphacki, thereby replacing pentagrams by pentagons, resp. replacing sissid by gad, and stip by pip.


Incidence matrix according to Dynkin symbol

x5/2o5o5/2x

.   . .   . | 1440 |    5    5 |    5   10    5 |   1   5   5   1
------------+------+-----------+----------------+----------------
x   . .   . |    2 | 3600    * |    2    2    0 |   1   2   1   0
.   . .   x |    2 |    * 3600 |    0    2    2 |   0   1   2   1
------------+------+-----------+----------------+----------------
x5/2o .   . |    5 |    5    0 | 1440    *    * |   1   1   0   0
x   . .   x |    4 |    2    2 |    * 3600    * |   0   1   1   0
.   . o5/2x |    5 |    0    5 |    *    * 1440 |   0   0   1   1
------------+------+-----------+----------------+----------------
x5/2o5o   .    12 |   30    0 |   12    0    0 | 120   *   *   *
x5/2o .   x    10 |   10    5 |    2    5    0 |   * 720   *   *
x   . o5/2x    10 |    5   10 |    0    5    2 |   *   * 720   *
.   o5o5/2x    12 |    0   30 |    0    0   12 |   *   *   * 120
or
.   . .   .    | 1440 |   10 |   10   10 |   2   10
---------------+------+------+-----------+---------
x   . .   .  & |    2 | 7200 |    2    2 |   1    3
---------------+------+------+-----------+---------
x5/2o .   .  & |    5 |    5 | 2880    * |   1    1
x   . .   x    |    4 |    4 |    * 3600 |   0    2
---------------+------+------+-----------+---------
x5/2o5o   .  &    12 |   30 |   12    0 | 240    *
x5/2o .   x  &    10 |   15 |    2    5 |   * 1440

x5/2o5/4o5/3x

.   .   .   . | 1440 |    5    5 |    5   10    5 |   1   5   5   1
--------------+------+-----------+----------------+----------------
x   .   .   . |    2 | 3600    * |    2    2    0 |   1   2   1   0
.   .   .   x |    2 |    * 3600 |    0    2    2 |   0   1   2   1
--------------+------+-----------+----------------+----------------
x5/2o   .   . |    5 |    5    0 | 1440    *    * |   1   1   0   0
x   .   .   x |    4 |    2    2 |    * 3600    * |   0   1   1   0
.   .   o5/3x |    5 |    0    5 |    *    * 1440 |   0   0   1   1
--------------+------+-----------+----------------+----------------
x5/2o5/4o   .    12 |   30    0 |   12    0    0 | 120   *   *   *
x5/2o   .   x    10 |   10    5 |    2    5    0 |   * 720   *   *
x   .   o5/3x    10 |    5   10 |    0    5    2 |   *   * 720   *
.   o5/4o5/3x    12 |    0   30 |    0    0   12 |   *   *   * 120

x5/3o5o5/3x

.   . .   . | 1440 |    5    5 |    5   10    5 |   1   5   5   1
------------+------+-----------+----------------+----------------
x   . .   . |    2 | 3600    * |    2    2    0 |   1   2   1   0
.   . .   x |    2 |    * 3600 |    0    2    2 |   0   1   2   1
------------+------+-----------+----------------+----------------
x5/3o .   . |    5 |    5    0 | 1440    *    * |   1   1   0   0
x   . .   x |    4 |    2    2 |    * 3600    * |   0   1   1   0
.   . o5/3x |    5 |    0    5 |    *    * 1440 |   0   0   1   1
------------+------+-----------+----------------+----------------
x5/3o5o   .    12 |   30    0 |   12    0    0 | 120   *   *   *
x5/3o .   x    10 |   10    5 |    2    5    0 |   * 720   *   *
x   . o5/3x    10 |    5   10 |    0    5    2 |   *   * 720   *
.   o5o5/3x    12 |    0   30 |    0    0   12 |   *   *   * 120
or
.   . .   .    | 1440 |   10 |   10   10 |   2   10
---------------+------+------+-----------+---------
x   . .   .  & |    2 | 7200 |    2    2 |   1    3
---------------+------+------+-----------+---------
x5/3o .   .  & |    5 |    5 | 2880    * |   1    1
x   . .   x    |    4 |    4 |    * 3600 |   0    2
---------------+------+------+-----------+---------
x5/3o5o   .  &    12 |   30 |   12    0 | 240    *
x5/3o .   x  &    10 |   15 |    2    5 |   * 1440

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