Acronym qrigfix (old: querfix)
Name quasirhombated great faceted hexacosachoron
Circumradius sqrt[10-4 sqrt(5)] = 1.027486

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


Incidence matrix according to Dynkin symbol

x3o5/3x5o
  
. .   . . | 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
----------+------+-----------+---------------------+------------
x3o   . . |    3 |    3    0 | 1200    *    *    * |   2   0   0
x .   x . |    4 |    2    2 |    * 3600    *    * |   1   1   0
. o5/3x . |    5 |    0    5 |    *    * 1440    * |   1   0   1
. .   x5o |    5 |    0    5 |    *    *    * 1440 |   0   1   1
----------+------+-----------+---------------------+------------
x3o5/3x .    60 |   60   60 |   20   30   12    0 | 120   *   *
x .   x5o    10 |    5   10 |    0    5    0    2 |   * 720   *
. o5/3x5o    30 |    0   60 |    0    0   12   12 |   *   * 120

x3o5/3x5/4o

. .   .   . | 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
------------+------+-----------+---------------------+------------
x3o   .   . |    3 |    3    0 | 1200    *    *    * |   2   0   0
x .   x   . |    4 |    2    2 |    * 3600    *    * |   1   1   0
. o5/3x   . |    5 |    0    5 |    *    * 1440    * |   1   0   1
. .   x5/4o |    5 |    0    5 |    *    *    * 1440 |   0   1   1
------------+------+-----------+---------------------+------------
x3o5/3x   .    60 |   60   60 |   20   30   12    0 | 120   *   *
x .   x5/4o    10 |    5   10 |    0    5    0    2 |   * 720   *
. o5/3x5/4o    30 |    0   60 |    0    0   12   12 |   *   * 120

x3/2o5/2x5o

.   .   . . | 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
------------+------+-----------+---------------------+------------
x3/2o   . . |    3 |    3    0 | 1200    *    *    * |   2   0   0
x   .   x . |    4 |    2    2 |    * 3600    *    * |   1   1   0
.   o5/2x . |    5 |    0    5 |    *    * 1440    * |   1   0   1
.   .   x5o |    5 |    0    5 |    *    *    * 1440 |   0   1   1
------------+------+-----------+---------------------+------------
x3/2o5/2x .    60 |   60   60 |   20   30   12    0 | 120   *   *
x   .   x5o    10 |    5   10 |    0    5    0    2 |   * 720   *
.   o5/2x5o    30 |    0   60 |    0    0   12   12 |   *   * 120

x3/2o5/2x5/4o

.   .   .   . | 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
--------------+------+-----------+---------------------+------------
x3/2o   .   . |    3 |    3    0 | 1200    *    *    * |   2   0   0
x   .   x   . |    4 |    2    2 |    * 3600    *    * |   1   1   0
.   o5/2x   . |    5 |    0    5 |    *    * 1440    * |   1   0   1
.   .   x5/4o |    5 |    0    5 |    *    *    * 1440 |   0   1   1
--------------+------+-----------+---------------------+------------
x3/2o5/2x   .    60 |   60   60 |   20   30   12    0 | 120   *   *
x   .   x5/4o    10 |    5   10 |    0    5    0    2 |   * 720   *
.   o5/2x5/4o    30 |    0   60 |    0    0   12   12 |   *   * 120

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