Acronym qracorn
Name quasiretrocellirhombated penteract
Circumradius sqrt[17-8 sqrt(2)]/2 = 1.192297
Coordinates (2 sqrt(2)-1, sqrt(2)-1, sqrt(2)-1, 1, 1)/2   & all permutations, all changes of sign
Colonel of regiment wacbinant
Face vector 960, 3840, 4400, 1760, 212

As abstract polytope qracorn is isomorph to sircarn, thereby replacing querco by sirco, resp. paqrit by prit and qrit by srit.


Incidence matrix according to Dynkin symbol

    3   3  4/3   
  x---x---o---x 
 3 \ / 3/2      
    o           
x4/3o3x3x3o3/2*c

.   . . . .      | 960 |   2    4   2 |   1   4   4   2   4   2   1 |  2   2   4   2   2   2   1   2 |  2  1  1  2  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x   . . . .      |   2 | 960    *   * |   1   2   2   0   0   0   0 |  2   2   2   1   1   0   0   0 |  2  1  1  1  0
.   . x . .      |   2 |   * 1920   * |   0   1   0   1   1   1   0 |  1   0   1   1   0   1   1   1 |  1  1  0  1  1
.   . . x .      |   2 |   *    * 960 |   0   0   2   0   2   0   1 |  0   1   2   0   2   1   0   2 |  1  0  1  2  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x4/3o . . .      |   4 |   4    0   0 | 240   *   *   *   *   *   * |  2   2   0   0   0   0   0   0 |  2  1  1  0  0
x   . x . .      |   4 |   2    2   0 |   * 960   *   *   *   *   * |  1   0   1   1   0   0   0   0 |  1  1  0  1  0
x   . . x .      |   4 |   2    0   2 |   *   * 960   *   *   *   * |  0   1   1   0   1   0   0   0 |  1  0  1  1  0
.   o3x . .      |   3 |   0    3   0 |   *   *   * 640   *   *   * |  1   0   0   0   0   1   1   0 |  1  1  0  0  1
.   . x3x .      |   6 |   0    3   3 |   *   *   *   * 640   *   * |  0   0   1   0   0   1   0   1 |  1  0  0  1  1
.   . x . o3/2*c |   3 |   0    3   0 |   *   *   *   *   * 640   * |  0   0   0   1   0   0   1   1 |  0  1  0  1  1
.   . . x3o      |   3 |   0    0   3 |   *   *   *   *   *   * 320 |  0   0   0   0   2   0   0   2 |  0  0  1  2  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x4/3o3x . .        24 |  24   24   0 |   6  12   0   8   0   0   0 | 80   *   *   *   *   *   *   * |  1  1  0  0  0
x4/3o . x .         8 |   8    0   4 |   2   0   4   0   0   0   0 |  * 240   *   *   *   *   *   * |  1  0  1  0  0
x   . x3x .        12 |   6    6   6 |   0   3   3   0   2   0   0 |  *   * 320   *   *   *   *   * |  1  0  0  1  0
x   . x . o3/2*c    6 |   3    6   0 |   0   3   0   0   0   2   0 |  *   *   * 320   *   *   *   * |  0  1  0  1  0
x   . . x3o         6 |   3    0   6 |   0   0   3   0   0   0   2 |  *   *   *   * 320   *   *   * |  0  0  1  1  0
.   o3x3x .        12 |   0   12   6 |   0   0   0   4   4   0   0 |  *   *   *   *   * 160   *   * |  1  0  0  0  1
.   o3x . o3/2*c    6 |   0   12   0 |   0   0   0   4   0   4   0 |  *   *   *   *   *   * 160   * |  0  1  0  0  1
.   . x3x3o3/2*c   12 |   0   12  12 |   0   0   0   0   4   4   4 |  *   *   *   *   *   *   * 160 |  0  0  0  1  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x4/3o3x3x .       192 | 192  192  96 |  48  96  96  64  64   0   0 |  8  24  32   0   0  16   0   0 | 10  *  *  *  *
x4/3o3x . o3/2*c   96 |  96  192   0 |  24  96   0  64   0  64   0 |  8   0   0  32   0   0  16   0 |  * 10  *  *  *
x4/3o . x3o        12 |  12    0  12 |   3   0  12   0   0   0   4 |  0   3   0   0   4   0   0   0 |  *  * 80  *  *
x   . x3x3o3/2*c   24 |  12   24  24 |   0  12  12   0   8   8   8 |  0   0   4   4   4   0   0   2 |  *  *  * 80  *
.   o3x3x3o3/2*c   30 |   0   60  30 |   0   0   0  20  20  20  10 |  0   0   0   0   0   5   5   5 |  *  *  *  * 32

  4/3  3   3     
 x---o---x---x   
        3 \ / 3/2
           o     
x4/3o3x3x3/2o3/2*c

.   . . .   .    | 960 |   2    4   2 |   1   4   4   2   4   2   1 |  2   2   4   2   2   2   1   2 |  2  1  1  2  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x   . . .   .    |   2 | 960    *   * |   1   2   2   0   0   0   0 |  2   2   2   1   1   0   0   0 |  2  1  1  1  0
.   . x .   .    |   2 |   * 1920   * |   0   1   0   1   1   1   0 |  1   0   1   1   0   1   1   1 |  1  1  0  1  1
.   . . x   .    |   2 |   *    * 960 |   0   0   2   0   2   0   1 |  0   1   2   0   2   1   0   2 |  1  0  1  2  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x4/3o . .   .    |   4 |   4    0   0 | 240   *   *   *   *   *   * |  2   2   0   0   0   0   0   0 |  2  1  1  0  0
x   . x .   .    |   4 |   2    2   0 |   * 960   *   *   *   *   * |  1   0   1   1   0   0   0   0 |  1  1  0  1  0
x   . . x   .    |   4 |   2    0   2 |   *   * 960   *   *   *   * |  0   1   1   0   1   0   0   0 |  1  0  1  1  0
.   o3x .   .    |   3 |   0    3   0 |   *   *   * 640   *   *   * |  1   0   0   0   0   1   1   0 |  1  1  0  0  1
.   . x3x   .    |   6 |   0    3   3 |   *   *   *   * 640   *   * |  0   0   1   0   0   1   0   1 |  1  0  0  1  1
.   . x .   o3*c |   3 |   0    3   0 |   *   *   *   *   * 640   * |  0   0   0   1   0   0   1   1 |  0  1  0  1  1
.   . . x3/2o    |   3 |   0    0   3 |   *   *   *   *   *   * 320 |  0   0   0   0   2   0   0   2 |  0  0  1  2  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x4/3o3x .   .      24 |  24   24   0 |   6  12   0   8   0   0   0 | 80   *   *   *   *   *   *   * |  1  1  0  0  0
x4/3o . x   .       8 |   8    0   4 |   2   0   4   0   0   0   0 |  * 240   *   *   *   *   *   * |  1  0  1  0  0
x   . x3x   .      12 |   6    6   6 |   0   3   3   0   2   0   0 |  *   * 320   *   *   *   *   * |  1  0  0  1  0
x   . x .   o3*c    6 |   3    6   0 |   0   3   0   0   0   2   0 |  *   *   * 320   *   *   *   * |  0  1  0  1  0
x   . . x3/2o       6 |   3    0   6 |   0   0   3   0   0   0   2 |  *   *   *   * 320   *   *   * |  0  0  1  1  0
.   o3x3x   .      12 |   0   12   6 |   0   0   0   4   4   0   0 |  *   *   *   *   * 160   *   * |  1  0  0  0  1
.   o3x .   o3*c    6 |   0   12   0 |   0   0   0   4   0   4   0 |  *   *   *   *   *   * 160   * |  0  1  0  0  1
.   . x3x3/2o3*c   12 |   0   12  12 |   0   0   0   0   4   4   4 |  *   *   *   *   *   *   * 160 |  0  0  0  1  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x4/3o3x3x   .     192 | 192  192  96 |  48  96  96  64  64   0   0 |  8  24  32   0   0  16   0   0 | 10  *  *  *  *
x4/3o3x .   o3*c   96 |  96  192   0 |  24  96   0  64   0  64   0 |  8   0   0  32   0   0  16   0 |  * 10  *  *  *
x4/3o . x3/2o      12 |  12    0  12 |   3   0  12   0   0   0   4 |  0   3   0   0   4   0   0   0 |  *  * 80  *  *
x   . x3x3/2o3*c   24 |  12   24  24 |   0  12  12   0   8   8   8 |  0   0   4   4   4   0   0   2 |  *  *  * 80  *
.   o3x3x3/2o3*c   30 |   0   60  30 |   0   0   0  20  20  20  10 |  0   0   0   0   0   5   5   5 |  *  *  *  * 32

    3  3/2  4   
  x---x---o---x 
 3 \ / 3/2      
    o           
x4o3/2x3x3o3/2*c

. .   . . .      | 960 |   2    4   2 |   1   4   4   2   4   2   1 |  2   2   4   2   2   2   1   2 |  2  1  1  2  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x .   . . .      |   2 | 960    *   * |   1   2   2   0   0   0   0 |  2   2   2   1   1   0   0   0 |  2  1  1  1  0
. .   x . .      |   2 |   * 1920   * |   0   1   0   1   1   1   0 |  1   0   1   1   0   1   1   1 |  1  1  0  1  1
. .   . x .      |   2 |   *    * 960 |   0   0   2   0   2   0   1 |  0   1   2   0   2   1   0   2 |  1  0  1  2  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x4o   . . .      |   4 |   4    0   0 | 240   *   *   *   *   *   * |  2   2   0   0   0   0   0   0 |  2  1  1  0  0
x .   x . .      |   4 |   2    2   0 |   * 960   *   *   *   *   * |  1   0   1   1   0   0   0   0 |  1  1  0  1  0
x .   . x .      |   4 |   2    0   2 |   *   * 960   *   *   *   * |  0   1   1   0   1   0   0   0 |  1  0  1  1  0
. o3/2x . .      |   3 |   0    3   0 |   *   *   * 640   *   *   * |  1   0   0   0   0   1   1   0 |  1  1  0  0  1
. .   x3x .      |   6 |   0    3   3 |   *   *   *   * 640   *   * |  0   0   1   0   0   1   0   1 |  1  0  0  1  1
. .   x . o3/2*c |   3 |   0    3   0 |   *   *   *   *   * 640   * |  0   0   0   1   0   0   1   1 |  0  1  0  1  1
. .   . x3o      |   3 |   0    0   3 |   *   *   *   *   *   * 320 |  0   0   0   0   2   0   0   2 |  0  0  1  2  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x4o3/2x . .        24 |  24   24   0 |   6  12   0   8   0   0   0 | 80   *   *   *   *   *   *   * |  1  1  0  0  0
x4o   . x .         8 |   8    0   4 |   2   0   4   0   0   0   0 |  * 240   *   *   *   *   *   * |  1  0  1  0  0
x .   x3x .        12 |   6    6   6 |   0   3   3   0   2   0   0 |  *   * 320   *   *   *   *   * |  1  0  0  1  0
x .   x . o3/2*c    6 |   3    6   0 |   0   3   0   0   0   2   0 |  *   *   * 320   *   *   *   * |  0  1  0  1  0
x .   . x3o         6 |   3    0   6 |   0   0   3   0   0   0   2 |  *   *   *   * 320   *   *   * |  0  0  1  1  0
. o3/2x3x .        12 |   0   12   6 |   0   0   0   4   4   0   0 |  *   *   *   *   * 160   *   * |  1  0  0  0  1
. o3/2x . o3/2*c    6 |   0   12   0 |   0   0   0   4   0   4   0 |  *   *   *   *   *   * 160   * |  0  1  0  0  1
. .   x3x3o3/2*c   12 |   0   12  12 |   0   0   0   0   4   4   4 |  *   *   *   *   *   *   * 160 |  0  0  0  1  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x4o3/2x3x .       192 | 192  192  96 |  48  96  96  64  64   0   0 |  8  24  32   0   0  16   0   0 | 10  *  *  *  *
x4o3/2x . o3/2*c   96 |  96  192   0 |  24  96   0  64   0  64   0 |  8   0   0  32   0   0  16   0 |  * 10  *  *  *
x4o   . x3o        12 |  12    0  12 |   3   0  12   0   0   0   4 |  0   3   0   0   4   0   0   0 |  *  * 80  *  *
x .   x3x3o3/2*c   24 |  12   24  24 |   0  12  12   0   8   8   8 |  0   0   4   4   4   0   0   2 |  *  *  * 80  *
. o3/2x3x3o3/2*c   30 |   0   60  30 |   0   0   0  20  20  20  10 |  0   0   0   0   0   5   5   5 |  *  *  *  * 32

   4  3/2  3     
 x---o---x---x   
        3 \ / 3/2
           o     
x4o3/2x3x3/2o3/2*c

. .   . .   .    | 960 |   2    4   2 |   1   4   4   2   4   2   1 |  2   2   4   2   2   2   1   2 |  2  1  1  2  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x .   . .   .    |   2 | 960    *   * |   1   2   2   0   0   0   0 |  2   2   2   1   1   0   0   0 |  2  1  1  1  0
. .   x .   .    |   2 |   * 1920   * |   0   1   0   1   1   1   0 |  1   0   1   1   0   1   1   1 |  1  1  0  1  1
. .   . x   .    |   2 |   *    * 960 |   0   0   2   0   2   0   1 |  0   1   2   0   2   1   0   2 |  1  0  1  2  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x4o   . .   .    |   4 |   4    0   0 | 240   *   *   *   *   *   * |  2   2   0   0   0   0   0   0 |  2  1  1  0  0
x .   x .   .    |   4 |   2    2   0 |   * 960   *   *   *   *   * |  1   0   1   1   0   0   0   0 |  1  1  0  1  0
x .   . x   .    |   4 |   2    0   2 |   *   * 960   *   *   *   * |  0   1   1   0   1   0   0   0 |  1  0  1  1  0
. o3/2x .   .    |   3 |   0    3   0 |   *   *   * 640   *   *   * |  1   0   0   0   0   1   1   0 |  1  1  0  0  1
. .   x3x   .    |   6 |   0    3   3 |   *   *   *   * 640   *   * |  0   0   1   0   0   1   0   1 |  1  0  0  1  1
. .   x .   o3*c |   3 |   0    3   0 |   *   *   *   *   * 640   * |  0   0   0   1   0   0   1   1 |  0  1  0  1  1
. .   . x3/2o    |   3 |   0    0   3 |   *   *   *   *   *   * 320 |  0   0   0   0   2   0   0   2 |  0  0  1  2  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x4o3/2x .   .      24 |  24   24   0 |   6  12   0   8   0   0   0 | 80   *   *   *   *   *   *   * |  1  1  0  0  0
x4o   . x   .       8 |   8    0   4 |   2   0   4   0   0   0   0 |  * 240   *   *   *   *   *   * |  1  0  1  0  0
x .   x3x   .      12 |   6    6   6 |   0   3   3   0   2   0   0 |  *   * 320   *   *   *   *   * |  1  0  0  1  0
x .   x .   o3*c    6 |   3    6   0 |   0   3   0   0   0   2   0 |  *   *   * 320   *   *   *   * |  0  1  0  1  0
x .   . x3/2o       6 |   3    0   6 |   0   0   3   0   0   0   2 |  *   *   *   * 320   *   *   * |  0  0  1  1  0
. o3/2x3x   .      12 |   0   12   6 |   0   0   0   4   4   0   0 |  *   *   *   *   * 160   *   * |  1  0  0  0  1
. o3/2x .   o3*c    6 |   0   12   0 |   0   0   0   4   0   4   0 |  *   *   *   *   *   * 160   * |  0  1  0  0  1
. .   x3x3/2o3*c   12 |   0   12  12 |   0   0   0   0   4   4   4 |  *   *   *   *   *   *   * 160 |  0  0  0  1  1
-----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x4o3/2x3x   .     192 | 192  192  96 |  48  96  96  64  64   0   0 |  8  24  32   0   0  16   0   0 | 10  *  *  *  *
x4o3/2x .   o3*c   96 |  96  192   0 |  24  96   0  64   0  64   0 |  8   0   0  32   0   0  16   0 |  * 10  *  *  *
x4o   . x3/2o      12 |  12    0  12 |   3   0  12   0   0   0   4 |  0   3   0   0   4   0   0   0 |  *  * 80  *  *
x .   x3x3/2o3*c   24 |  12   24  24 |   0  12  12   0   8   8   8 |  0   0   4   4   4   0   0   2 |  *  *  * 80  *
. o3/2x3x3/2o3*c   30 |   0   60  30 |   0   0   0  20  20  20  10 |  0   0   0   0   0   5   5   5 |  *  *  *  * 32

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