Acronym	paqrit
Name	prismatoquasirhombated tesseract
Cross sections	©
Circumradius	sqrt[(7-3 sqrt(2))/2] = 1.174172
Coordinates	((2 sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2, 1/2)   & all permutations, all changes of sign
Colonel of regiment	gichado
Face vector	192, 480, 368, 80
Confer	general polytopal classes: Wythoffian polychora
External links

As abstract polytope paqrit is isomorphic to prit, thereby replacing querco by sirco. – As such paqrit is a lieutenant.

Incidence matrix according to Dynkin symbol

x3x3o4/3x

. . .   . | 192 |  1   2   2 |  2  2  1  2  1 |  1  2  1 1
----------+-----+------------+----------------+-----------
x . .   . |   2 | 96   *   * |  2  2  0  0  0 |  1  2  1 0
. x .   . |   2 |  * 192   * |  1  0  1  1  0 |  1  1  0 1
. . .   x |   2 |  *   * 192 |  0  1  0  1  1 |  0  1  1 1
----------+-----+------------+----------------+-----------
x3x .   . |   6 |  3   3   0 | 64  *  *  *  * |  1  1  0 0
x . .   x |   4 |  2   0   2 |  * 96  *  *  * |  0  1  1 0
. x3o   . |   3 |  0   3   0 |  *  * 64  *  * |  1  0  0 1
. x .   x |   4 |  0   2   2 |  *  *  * 96  * |  0  1  0 1
. . o4/3x |   4 |  0   0   4 |  *  *  *  * 48 |  0  0  1 1
----------+-----+------------+----------------+-----------
x3x3o   . ♦  12 |  6  12   0 |  4  0  4  0  0 | 16  *  * *
x3x .   x ♦  12 |  6   6   6 |  2  3  0  3  0 |  * 32  * *
x . o4/3x ♦   8 |  4   0   8 |  0  4  0  0  2 |  *  * 24 *
. x3o4/3x ♦  24 |  0  24  24 |  0  0  8 12  6 |  *  *  * 8

x3x3/2o4x

. .   . . | 192 |  1   2   2 |  2  2  1  2  1 |  1  2  1 1
----------+-----+------------+----------------+-----------
x .   . . |   2 | 96   *   * |  2  2  0  0  0 |  1  2  1 0
. x   . . |   2 |  * 192   * |  1  0  1  1  0 |  1  1  0 1
. .   . x |   2 |  *   * 192 |  0  1  0  1  1 |  0  1  1 1
----------+-----+------------+----------------+-----------
x3x   . . |   6 |  3   3   0 | 64  *  *  *  * |  1  1  0 0
x .   . x |   4 |  2   0   2 |  * 96  *  *  * |  0  1  1 0
. x3/2o . |   3 |  0   3   0 |  *  * 64  *  * |  1  0  0 1
. x   . x |   4 |  0   2   2 |  *  *  * 96  * |  0  1  0 1
. .   o4x |   4 |  0   0   4 |  *  *  *  * 48 |  0  0  1 1
----------+-----+------------+----------------+-----------
x3x3/2o . ♦  12 |  6  12   0 |  4  0  4  0  0 | 16  *  * *
x3x   . x ♦  12 |  6   6   6 |  2  3  0  3  0 |  * 32  * *
x .   o4x ♦   8 |  4   0   8 |  0  4  0  0  2 |  *  * 24 *
. x3/2o4x ♦  24 |  0  24  24 |  0  0  8 12  6 |  *  *  * 8