Acronym ...
Name 2sitphi (?)
Circumradius sqrt[3+sqrt(5)] = 2.288246
General of army hi
Colonel of regiment sidtaxhi
Confer
non-Grünbaumian master:
sitphi  

Looks like a compound of 2 small tripesic hecatonicosachora (sitphi), and indeed vertices coincide by 6, all other elements by 2.

As abstract polytope sitphi is isomorphic to gitphi, thereby replacing the decagons by decagrams and pentagrams by pentagons, resp. replacing tigid by quit sissid.


Incidence matrix according to Dynkin symbol

o5/2x5x5/2o

.   . .   . | 3600 |    2    2 |   1    4   1 |   2   2
------------+------+-----------+--------------+--------
.   x .   . |    2 | 3600    * |   1    2   0 |   2   1
.   . x   . |    2 |    * 3600 |   0    2   1 |   1   2
------------+------+-----------+--------------+--------
o5/2x .   . |    5 |    5    0 | 720    *   * |   2   0
.   x5x   . |   10 |    5    5 |   * 1440   * |   1   1
.   . x5/2o |    5 |    0    5 |   *    * 720 |   0   2
------------+------+-----------+--------------+--------
o5/2x5x   .    60 |   60   30 |  12   12   0 | 120   *
.   x5x5/2o    60 |   30   60 |   0   12  12 |   * 120
or
.   . .   .    | 3600 |    4 |    2    4 |   4
---------------+------+------+-----------+----
.   x .   .  & |    2 | 7200 |    1    2 |   3
---------------+------+------+-----------+----
o5/2x .   .  & |    5 |    5 | 1440    * |   2
.   x5x   .    |   10 |   10 |    * 1440 |   2
---------------+------+------+-----------+----
o5/2x5x   .  &    60 |   90 |   12   12 | 240

o5/2x5x5/3o

.   . .   . | 3600 |    2    2 |   1    4   1 |   2   2
------------+------+-----------+--------------+--------
.   x .   . |    2 | 3600    * |   1    2   0 |   2   1
.   . x   . |    2 |    * 3600 |   0    2   1 |   1   2
------------+------+-----------+--------------+--------
o5/2x .   . |    5 |    5    0 | 720    *   * |   2   0
.   x5x   . |   10 |    5    5 |   * 1440   * |   1   1
.   . x5/3o |    5 |    0    5 |   *    * 720 |   0   2
------------+------+-----------+--------------+--------
o5/2x5x   .    60 |   60   30 |  12   12   0 | 120   *
.   x5x5/3o    60 |   30   60 |   0   12  12 |   * 120

o5/3x5x5/3o

.   . .   . | 3600 |    2    2 |   1    4   1 |   2   2
------------+------+-----------+--------------+--------
.   x .   . |    2 | 3600    * |   1    2   0 |   2   1
.   . x   . |    2 |    * 3600 |   0    2   1 |   1   2
------------+------+-----------+--------------+--------
o5/3x .   . |    5 |    5    0 | 720    *   * |   2   0
.   x5x   . |   10 |    5    5 |   * 1440   * |   1   1
.   . x5/3o |    5 |    0    5 |   *    * 720 |   0   2
------------+------+-----------+--------------+--------
o5/3x5x   .    60 |   60   30 |  12   12   0 | 120   *
.   x5x5/3o    60 |   30   60 |   0   12  12 |   * 120
or
.   . .   .    | 3600 |    4 |    2    4 |   4
---------------+------+------+-----------+----
.   x .   .  & |    2 | 7200 |    1    2 |   3
---------------+------+------+-----------+----
o5/3x .   .  & |    5 |    5 | 1440    * |   2
.   x5x   .    |   10 |   10 |    * 1440 |   2
---------------+------+------+-----------+----
o5/3x5x   .  &    60 |   90 |   12   12 | 240

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