Acronym	quacrant
Name	quasicellirhombipenteractitriacontiditeron
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, 4720, 2080, 242
Confer	general polytopal classes: Wythoffian polytera
External links

As abstract polytope quacrant is isomorphic to carnit, thereby replacing querco with sirco, resp. quercope by sircope and qrit by srit. As such quacrant is a lieutenant.

Incidence matrix according to Dynkin symbol

x3o3x3o4/3x

. . . .   . | 960 |   2    4   2 |   1   4   4   2   2   4   1 |   2   2   2   4   2   1   2  2 |  1  2  1  2  1
------------+-----+--------------+-----------------------------+--------------------------------+---------------
x . . .   . |   2 | 960    *   * |   1   2   2   0   0   0   0 |   2   2   1   2   1   0   0  0 |  1  2  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   0   2   1 |   0   1   0   2   2   0   1  2 |  0  1  1  2  1
------------+-----+--------------+-----------------------------+--------------------------------+---------------
x3o . .   . |   3 |   3    0   0 | 320   *   *   *   *   *   * |   2   2   0   0   0   0   0  0 |  1  2  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   0   1   1   0   0  0 |  0  1  1  1  0
. o3x .   . |   3 |   0    3   0 |   *   *   * 640   *   *   * |   1   0   0   0   0   1   1  0 |  1  1  0  0  1
. . x3o   . |   3 |   0    3   0 |   *   *   *   * 640   *   * |   0   0   1   0   0   1   0  1 |  1  0  0  1  1
. . x .   x |   4 |   0    2   2 |   *   *   *   *   * 960   * |   0   0   0   1   0   0   1  1 |  0  1  0  1  1
. . . o4/3x |   4 |   0    0   4 |   *   *   *   *   *   * 240 |   0   0   0   0   2   0   0  2 |  0  0  1  2  1
------------+-----+--------------+-----------------------------+--------------------------------+---------------
x3o3x .   . ♦  12 |  12   12   0 |   4   6   0   4   0   0   0 | 160   *   *   *   *   *   *  * |  1  1  0  0  0
x3o . .   x ♦   6 |   6    0   3 |   2   0   3   0   0   0   0 |   * 320   *   *   *   *   *  * |  0  1  1  0  0
x . x3o   . ♦   6 |   3    6   0 |   0   3   0   0   2   0   0 |   *   * 320   *   *   *   *  * |  1  0  0  1  0
x . x .   x ♦   8 |   4    4   4 |   0   2   2   0   0   2   0 |   *   *   * 480   *   *   *  * |  0  1  0  1  0
x . . o4/3x ♦   8 |   4    0   8 |   0   0   4   0   0   0   2 |   *   *   *   * 240   *   *  * |  0  0  1  1  0
. o3x3o   . ♦   6 |   0   12   0 |   0   0   0   4   4   0   0 |   *   *   *   *   * 160   *  * |  1  0  0  0  1
. o3x .   x ♦   6 |   0    6   3 |   0   0   0   2   0   3   0 |   *   *   *   *   *   * 320  * |  0  1  0  0  1
. . x3o4/3x ♦  24 |   0   24  24 |   0   0   0   0   8  12   6 |   *   *   *   *   *   *   * 80 |  0  0  0  1  1
------------+-----+--------------+-----------------------------+--------------------------------+---------------
x3o3x3o   . ♦  30 |  30   60   0 |  10  30   0  20  20   0   0 |   5   0  10   0   0   5   0  0 | 32  *  *  *  *
x3o3x .   x ♦  24 |  24   24  12 |   8  12  12   8   0  12   0 |   2   4   0   6   0   0   4  0 |  * 80  *  *  *
x3o . o4/3x ♦  12 |  12    0  12 |   4   0  12   0   0   0   3 |   0   4   0   0   3   0   0  0 |  *  * 80  *  *
x . x3o4/3x ♦  48 |  24   48  48 |   0  24  24   0  16  24  12 |   0   0   8  12   6   0   0  2 |  *  *  * 40  *
. o3x3o4/3x ♦  96 |   0  192  96 |   0   0   0  64  64  96  24 |   0   0   0   0   0  16  32  8 |  *  *  *  * 10

x3o3x3/2o4x

. . .   . . | 960 |   2    4   2 |   1   4   4   2   2   4   1 |   2   2   2   4   2   1   2  2 |  1  2  1  2  1
------------+-----+--------------+-----------------------------+--------------------------------+---------------
x . .   . . |   2 | 960    *   * |   1   2   2   0   0   0   0 |   2   2   1   2   1   0   0  0 |  1  2  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   0   2   1 |   0   1   0   2   2   0   1  2 |  0  1  1  2  1
------------+-----+--------------+-----------------------------+--------------------------------+---------------
x3o .   . . |   3 |   3    0   0 | 320   *   *   *   *   *   * |   2   2   0   0   0   0   0  0 |  1  2  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   0   1   1   0   0  0 |  0  1  1  1  0
. o3x   . . |   3 |   0    3   0 |   *   *   * 640   *   *   * |   1   0   0   0   0   1   1  0 |  1  1  0  0  1
. . x3/2o . |   3 |   0    3   0 |   *   *   *   * 640   *   * |   0   0   1   0   0   1   0  1 |  1  0  0  1  1
. . x   . x |   4 |   0    2   2 |   *   *   *   *   * 960   * |   0   0   0   1   0   0   1  1 |  0  1  0  1  1
. . .   o4x |   4 |   0    0   4 |   *   *   *   *   *   * 240 |   0   0   0   0   2   0   0  2 |  0  0  1  2  1
------------+-----+--------------+-----------------------------+--------------------------------+---------------
x3o3x   . . ♦  12 |  12   12   0 |   4   6   0   4   0   0   0 | 160   *   *   *   *   *   *  * |  1  1  0  0  0
x3o .   . x ♦   6 |   6    0   3 |   2   0   3   0   0   0   0 |   * 320   *   *   *   *   *  * |  0  1  1  0  0
x . x3/2o . ♦   6 |   3    6   0 |   0   3   0   0   2   0   0 |   *   * 320   *   *   *   *  * |  1  0  0  1  0
x . x   . x ♦   8 |   4    4   4 |   0   2   2   0   0   2   0 |   *   *   * 480   *   *   *  * |  0  1  0  1  0
x . .   o4x ♦   8 |   4    0   8 |   0   0   4   0   0   0   2 |   *   *   *   * 240   *   *  * |  0  0  1  1  0
. o3x3/2o . ♦   6 |   0   12   0 |   0   0   0   4   4   0   0 |   *   *   *   *   * 160   *  * |  1  0  0  0  1
. o3x   . x ♦   6 |   0    6   3 |   0   0   0   2   0   3   0 |   *   *   *   *   *   * 320  * |  0  1  0  0  1
. . x3/2o4x ♦  24 |   0   24  24 |   0   0   0   0   8  12   6 |   *   *   *   *   *   *   * 80 |  0  0  0  1  1
------------+-----+--------------+-----------------------------+--------------------------------+---------------
x3o3x3/2o . ♦  30 |  30   60   0 |  10  30   0  20  20   0   0 |   5   0  10   0   0   5   0  0 | 32  *  *  *  *
x3o3x   . x ♦  24 |  24   24  12 |   8  12  12   8   0  12   0 |   2   4   0   6   0   0   4  0 |  * 80  *  *  *
x3o .   o4x ♦  12 |  12    0  12 |   4   0  12   0   0   0   3 |   0   4   0   0   3   0   0  0 |  *  * 80  *  *
x . x3/2o4x ♦  48 |  24   48  48 |   0  24  24   0  16  24  12 |   0   0   8  12   6   0   0  2 |  *  *  * 40  *
. o3x3/2o4x ♦  96 |   0  192  96 |   0   0   0  64  64  96  24 |   0   0   0   0   0  16  32  8 |  *  *  *  * 10

x3/2o3/2x3o4/3x

.   .   . .   . | 960 |   2    4   2 |   1   4   4   2   2   4   1 |   2   2   2   4   2   1   2  2 |  1  2  1  2  1
----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x   .   . .   . |   2 | 960    *   * |   1   2   2   0   0   0   0 |   2   2   1   2   1   0   0  0 |  1  2  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   0   2   1 |   0   1   0   2   2   0   1  2 |  0  1  1  2  1
----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x3/2o   . .   . |   3 |   3    0   0 | 320   *   *   *   *   *   * |   2   2   0   0   0   0   0  0 |  1  2  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   0   1   1   0   0  0 |  0  1  1  1  0
.   o3/2x .   . |   3 |   0    3   0 |   *   *   * 640   *   *   * |   1   0   0   0   0   1   1  0 |  1  1  0  0  1
.   .   x3o   . |   3 |   0    3   0 |   *   *   *   * 640   *   * |   0   0   1   0   0   1   0  1 |  1  0  0  1  1
.   .   x .   x |   4 |   0    2   2 |   *   *   *   *   * 960   * |   0   0   0   1   0   0   1  1 |  0  1  0  1  1
.   .   . o4/3x |   4 |   0    0   4 |   *   *   *   *   *   * 240 |   0   0   0   0   2   0   0  2 |  0  0  1  2  1
----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x3/2o3/2x .   . ♦  12 |  12   12   0 |   4   6   0   4   0   0   0 | 160   *   *   *   *   *   *  * |  1  1  0  0  0
x3/2o   . .   x ♦   6 |   6    0   3 |   2   0   3   0   0   0   0 |   * 320   *   *   *   *   *  * |  0  1  1  0  0
x   .   x3o   . ♦   6 |   3    6   0 |   0   3   0   0   2   0   0 |   *   * 320   *   *   *   *  * |  1  0  0  1  0
x   .   x .   x ♦   8 |   4    4   4 |   0   2   2   0   0   2   0 |   *   *   * 480   *   *   *  * |  0  1  0  1  0
x   .   . o4/3x ♦   8 |   4    0   8 |   0   0   4   0   0   0   2 |   *   *   *   * 240   *   *  * |  0  0  1  1  0
.   o3/2x3o   . ♦   6 |   0   12   0 |   0   0   0   4   4   0   0 |   *   *   *   *   * 160   *  * |  1  0  0  0  1
.   o3/2x .   x ♦   6 |   0    6   3 |   0   0   0   2   0   3   0 |   *   *   *   *   *   * 320  * |  0  1  0  0  1
.   .   x3o4/3x ♦  24 |   0   24  24 |   0   0   0   0   8  12   6 |   *   *   *   *   *   *   * 80 |  0  0  0  1  1
----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x3/2o3/2x3o   . ♦  30 |  30   60   0 |  10  30   0  20  20   0   0 |   5   0  10   0   0   5   0  0 | 32  *  *  *  *
x3/2o3/2x .   x ♦  24 |  24   24  12 |   8  12  12   8   0  12   0 |   2   4   0   6   0   0   4  0 |  * 80  *  *  *
x3/2o   . o4/3x ♦  12 |  12    0  12 |   4   0  12   0   0   0   3 |   0   4   0   0   3   0   0  0 |  *  * 80  *  *
x   .   x3o4/3x ♦  48 |  24   48  48 |   0  24  24   0  16  24  12 |   0   0   8  12   6   0   0  2 |  *  *  * 40  *
.   o3/2x3o4/3x ♦  96 |   0  192  96 |   0   0   0  64  64  96  24 |   0   0   0   0   0  16  32  8 |  *  *  *  * 10

x3/2o3/2x3/2o4x

.   .   .   . . | 960 |   2    4   2 |   1   4   4   2   2   4   1 |   2   2   2   4   2   1   2  2 |  1  2  1  2  1
----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x   .   .   . . |   2 | 960    *   * |   1   2   2   0   0   0   0 |   2   2   1   2   1   0   0  0 |  1  2  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   0   2   1 |   0   1   0   2   2   0   1  2 |  0  1  1  2  1
----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x3/2o   .   . . |   3 |   3    0   0 | 320   *   *   *   *   *   * |   2   2   0   0   0   0   0  0 |  1  2  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   0   1   1   0   0  0 |  0  1  1  1  0
.   o3/2x   . . |   3 |   0    3   0 |   *   *   * 640   *   *   * |   1   0   0   0   0   1   1  0 |  1  1  0  0  1
.   .   x3/2o . |   3 |   0    3   0 |   *   *   *   * 640   *   * |   0   0   1   0   0   1   0  1 |  1  0  0  1  1
.   .   x   . x |   4 |   0    2   2 |   *   *   *   *   * 960   * |   0   0   0   1   0   0   1  1 |  0  1  0  1  1
.   .   .   o4x |   4 |   0    0   4 |   *   *   *   *   *   * 240 |   0   0   0   0   2   0   0  2 |  0  0  1  2  1
----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x3/2o3/2x   . . ♦  12 |  12   12   0 |   4   6   0   4   0   0   0 | 160   *   *   *   *   *   *  * |  1  1  0  0  0
x3/2o   .   . x ♦   6 |   6    0   3 |   2   0   3   0   0   0   0 |   * 320   *   *   *   *   *  * |  0  1  1  0  0
x   .   x3/2o . ♦   6 |   3    6   0 |   0   3   0   0   2   0   0 |   *   * 320   *   *   *   *  * |  1  0  0  1  0
x   .   x   . x ♦   8 |   4    4   4 |   0   2   2   0   0   2   0 |   *   *   * 480   *   *   *  * |  0  1  0  1  0
x   .   .   o4x ♦   8 |   4    0   8 |   0   0   4   0   0   0   2 |   *   *   *   * 240   *   *  * |  0  0  1  1  0
.   o3/2x3/2o . ♦   6 |   0   12   0 |   0   0   0   4   4   0   0 |   *   *   *   *   * 160   *  * |  1  0  0  0  1
.   o3/2x   . x ♦   6 |   0    6   3 |   0   0   0   2   0   3   0 |   *   *   *   *   *   * 320  * |  0  1  0  0  1
.   .   x3/2o4x ♦  24 |   0   24  24 |   0   0   0   0   8  12   6 |   *   *   *   *   *   *   * 80 |  0  0  0  1  1
----------------+-----+--------------+-----------------------------+--------------------------------+---------------
x3/2o3/2x3/2o . ♦  30 |  30   60   0 |  10  30   0  20  20   0   0 |   5   0  10   0   0   5   0  0 | 32  *  *  *  *
x3/2o3/2x   . x ♦  24 |  24   24  12 |   8  12  12   8   0  12   0 |   2   4   0   6   0   0   4  0 |  * 80  *  *  *
x3/2o   .   o4x ♦  12 |  12    0  12 |   4   0  12   0   0   0   3 |   0   4   0   0   3   0   0  0 |  *  * 80  *  *
x   .   x3/2o4x ♦  48 |  24   48  48 |   0  24  24   0  16  24  12 |   0   0   8  12   6   0   0  2 |  *  *  * 40  *
.   o3/2x3/2o4x ♦  96 |   0  192  96 |   0   0   0  64  64  96  24 |   0   0   0   0   0  16  32  8 |  *  *  *  * 10