Acronym	qrit
Name	quasirhombated tesseract
Cross sections	©
Circumradius	sqrt[2-sqrt(2)] = 0.765367
Inradius wrt. oct	1-1/sqrt(2) = 0.292893
Inradius wrt. querco	(sqrt(2)-1)/2 = 0.207107
Inradius wrt. trip	sqrt[(17-12 sqrt(2))/12] = 0.0495288
Coordinates	((sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2, 1/2)   & all permutations, all changes of sign
Volume	[32 sqrt(2)-45]/3 = 0.0849447
General of army	srit
Colonel of regiment	wavitoth
Dihedral angles (at margins)	at {4} between querco and querco:   90° at {3} between oct and querco:   60° at {4} between trip and querco:   arccos[1/sqrt(3)] = 54.735610° at {3} between oct and trip:   30°
Face vector	96, 288, 248, 56
Confer	general polytopal classes: Wythoffian polychora   analogs: quasirhombated hypercube qrbCn
External links

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

Incidence matrix according to Dynkin symbol

o3x3o4/3x

. . .   . | 96 |   4  2 |  2  2  4  1 |  1  2 2
----------+----+--------+-------------+--------
. x .   . |  2 | 192  * |  1  1  1  0 |  1  1 1
. . .   x |  2 |   * 96 |  0  0  2  1 |  0  1 2
----------+----+--------+-------------+--------
o3x .   . |  3 |   3  0 | 64  *  *  * |  1  1 0
. x3o   . |  3 |   3  0 |  * 64  *  * |  1  0 1
. x .   x |  4 |   2  2 |  *  * 96  * |  0  1 1
. . o4/3x |  4 |   0  4 |  *  *  * 24 |  0  0 2
----------+----+--------+-------------+--------
o3x3o   . ♦  6 |  12  0 |  4  4  0  0 | 16  * *
o3x .   x ♦  6 |   6  3 |  2  0  3  0 |  * 32 *
. x3o4/3x ♦ 24 |  24 24 |  0  8 12  6 |  *  * 8

o3x3/2o4x

. .   . . | 96 |   4  2 |  2  2  4  1 |  1  2 2
----------+----+--------+-------------+--------
. x   . . |  2 | 192  * |  1  1  1  0 |  1  1 1
. .   . x |  2 |   * 96 |  0  0  2  1 |  0  1 2
----------+----+--------+-------------+--------
o3x   . . |  3 |   3  0 | 64  *  *  * |  1  1 0
. x3/2o . |  3 |   3  0 |  * 64  *  * |  1  0 1
. x   . x |  4 |   2  2 |  *  * 96  * |  0  1 1
. .   o4x |  4 |   0  4 |  *  *  * 24 |  0  0 2
----------+----+--------+-------------+--------
o3x3/2o . ♦  6 |  12  0 |  4  4  0  0 | 16  * *
o3x   . x ♦  6 |   6  3 |  2  0  3  0 |  * 32 *
. x3/2o4x ♦ 24 |  24 24 |  0  8 12  6 |  *  * 8

o3/2x3o4/3x

.   . .   . | 96 |   4  2 |  2  2  4  1 |  1  2 2
------------+----+--------+-------------+--------
.   x .   . |  2 | 192  * |  1  1  1  0 |  1  1 1
.   . .   x |  2 |   * 96 |  0  0  2  1 |  0  1 2
------------+----+--------+-------------+--------
o3/2x .   . |  3 |   3  0 | 64  *  *  * |  1  1 0
.   x3o   . |  3 |   3  0 |  * 64  *  * |  1  0 1
.   x .   x |  4 |   2  2 |  *  * 96  * |  0  1 1
.   . o4/3x |  4 |   0  4 |  *  *  * 24 |  0  0 2
------------+----+--------+-------------+--------
o3/2x3o   . ♦  6 |  12  0 |  4  4  0  0 | 16  * *
o3/2x .   x ♦  6 |   6  3 |  2  0  3  0 |  * 32 *
.   x3o4/3x ♦ 24 |  24 24 |  0  8 12  6 |  *  * 8

o3/2x3/2o4x

.   .   . . | 96 |   4  2 |  2  2  4  1 |  1  2 2
------------+----+--------+-------------+--------
.   x   . . |  2 | 192  * |  1  1  1  0 |  1  1 1
.   .   . x |  2 |   * 96 |  0  0  2  1 |  0  1 2
------------+----+--------+-------------+--------
o3/2x   . . |  3 |   3  0 | 64  *  *  * |  1  1 0
.   x3/2o . |  3 |   3  0 |  * 64  *  * |  1  0 1
.   x   . x |  4 |   2  2 |  *  * 96  * |  0  1 1
.   .   o4x |  4 |   0  4 |  *  *  * 24 |  0  0 2
------------+----+--------+-------------+--------
o3/2x3/2o . ♦  6 |  12  0 |  4  4  0  0 | 16  * *
o3/2x   . x ♦  6 |   6  3 |  2  0  3  0 |  * 32 *
.   x3/2o4x ♦ 24 |  24 24 |  0  8 12  6 |  *  * 8