Acronym qragishi (old: qraghi)
Name quasirhombated grand stellated hecatonicosachoron
Circumradius sqrt[5-sqrt(5)] = 1.662508

As abstract polytope qragishi is isomorphic to sraghi, thereby interchanging pentagrams and pentagons, resp. replacing pip by stip, qrid by srid, and id by gid. – As such qragishi is a lieutenant.


Incidence matrix according to Dynkin symbol

x5/2o3/2x5o
  
.   .   . . | 3600 |    2    4 |   1    4    2    2 |   2   2   1
------------+------+-----------+--------------------+------------
x   .   . . |    2 | 3600    * |   1    2    0    0 |   2   1   0
.   .   x . |    2 |    * 7200 |   0    1    1    1 |   1   1   1
------------+------+-----------+--------------------+------------
x5/2o   . . |    5 |    5    0 | 720    *    *    * |   2   0   0
x   .   x . |    4 |    2    2 |   * 3600    *    * |   1   1   0
.   o3/2x . |    3 |    0    3 |   *    * 2400    * |   1   0   1
.   .   x5o |    5 |    0    5 |   *    *    * 1440 |   0   1   1
------------+------+-----------+--------------------+------------
x5/2o3/2x .    60 |   60   60 |  12   30   20    0 | 120   *   *
x   .   x5o    10 |    5   10 |   0    5    0    2 |   * 720   *
.   o3/2x5o    30 |    0   60 |   0    0   20   12 |   *   * 120

x5/2o3/2x5/4o
  
.   .   .   . | 3600 |    2    4 |   1    4    2    2 |   2   2   1
--------------+------+-----------+--------------------+------------
x   .   .   . |    2 | 3600    * |   1    2    0    0 |   2   1   0
.   .   x   . |    2 |    * 7200 |   0    1    1    1 |   1   1   1
--------------+------+-----------+--------------------+------------
x5/2o   .   . |    5 |    5    0 | 720    *    *    * |   2   0   0
x   .   x   . |    4 |    2    2 |   * 3600    *    * |   1   1   0
.   o3/2x   . |    3 |    0    3 |   *    * 2400    * |   1   0   1
.   .   x5/4o |    5 |    0    5 |   *    *    * 1440 |   0   1   1
--------------+------+-----------+--------------------+------------
x5/2o3/2x   .    60 |   60   60 |  12   30   20    0 | 120   *   *
x   .   x5/4o    10 |    5   10 |   0    5    0    2 |   * 720   *
.   o3/2x5/4o    30 |    0   60 |   0    0   20   12 |   *   * 120

x5/3o3x5o
  
.   . . . | 3600 |    2    4 |   1    4    2    2 |   2   2   1
----------+------+-----------+--------------------+------------
x   . . . |    2 | 3600    * |   1    2    0    0 |   2   1   0
.   . x . |    2 |    * 7200 |   0    1    1    1 |   1   1   1
----------+------+-----------+--------------------+------------
x5/3o . . |    5 |    5    0 | 720    *    *    * |   2   0   0
x   . x . |    4 |    2    2 |   * 3600    *    * |   1   1   0
.   o3x . |    3 |    0    3 |   *    * 2400    * |   1   0   1
.   . x5o |    5 |    0    5 |   *    *    * 1440 |   0   1   1
----------+------+-----------+--------------------+------------
x5/3o3x .    60 |   60   60 |  12   30   20    0 | 120   *   *
x   . x5o    10 |    5   10 |   0    5    0    2 |   * 720   *
.   o3x5o    30 |    0   60 |   0    0   20   12 |   *   * 120

x5/3o3x5/4o
  
.   . .   . | 3600 |    2    4 |   1    4    2    2 |   2   2   1
------------+------+-----------+--------------------+------------
x   . .   . |    2 | 3600    * |   1    2    0    0 |   2   1   0
.   . x   . |    2 |    * 7200 |   0    1    1    1 |   1   1   1
------------+------+-----------+--------------------+------------
x5/3o .   . |    5 |    5    0 | 720    *    *    * |   2   0   0
x   . x   . |    4 |    2    2 |   * 3600    *    * |   1   1   0
.   o3x   . |    3 |    0    3 |   *    * 2400    * |   1   0   1
.   . x5/4o |    5 |    0    5 |   *    *    * 1440 |   0   1   1
------------+------+-----------+--------------------+------------
x5/3o3x   .    60 |   60   60 |  12   30   20    0 | 120   *   *
x   . x5/4o    10 |    5   10 |   0    5    0    2 |   * 720   *
.   o3x5/4o    30 |    0   60 |   0    0   20   12 |   *   * 120

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