Acronym	quiproh
Name	quasiprismatorhombated hexadecachoron
Circumradius	sqrt[4-2 sqrt(2)] = 1.082392
Coordinates	((2 sqrt(2)-1)/2, (sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2)   & all permutations, all changes of sign
Colonel of regiment	(is itself locally convex – uniform polychoral members: by cells: co oho quitco quith stop trip quiproh 16 0 0 8 24 32 giphado 0 16 8 8 0 32   & others)
External links

As abstract polytope quiproh is isomorphic to proh, thereby replacing octagrams by octagons, resp. replacing quith by tic and replacing stop by op. – As such quiproh is a lieutenant.

Incidence matrix according to Dynkin symbol

x3o3x4/3x

. . .   . | 192 |   2   2  1 |  1  2  2  1  2 |  1  1  2 1
----------+-----+------------+----------------+-----------
x . .   . |   2 | 192   *  * |  1  1  1  0  0 |  1  1  1 0
. . x   . |   2 |   * 192  * |  0  1  0  1  1 |  1  0  1 1
. . .   x |   2 |   *   * 96 |  0  0  2  0  2 |  0  1  2 1
----------+-----+------------+----------------+-----------
x3o .   . |   3 |   3   0  0 | 64  *  *  *  * |  1  1  0 0
x . x   . |   4 |   2   2  0 |  * 96  *  *  * |  1  0  1 0
x . .   x |   4 |   2   0  2 |  *  * 96  *  * |  0  1  1 0
. o3x   . |   3 |   0   3  0 |  *  *  * 64  * |  1  0  0 1
. . x4/3x |   8 |   0   4  4 |  *  *  *  * 48 |  0  0  1 1
----------+-----+------------+----------------+-----------
x3o3x   . ♦  12 |  12  12  0 |  4  6  0  4  0 | 16  *  * *
x3o .   x ♦   6 |   6   0  3 |  2  0  3  0  0 |  * 32  * *
x . x4/3x ♦  16 |   8   8  8 |  0  4  4  0  2 |  *  * 24 *
. o3x4/3x ♦  24 |   0  24 12 |  0  0  0  8  6 |  *  *  * 8

x3/2o3/2x4/3x

.   .   .   . | 192 |   2   2  1 |  1  2  2  1  2 |  1  1  2 1
--------------+-----+------------+----------------+-----------
x   .   .   . |   2 | 192   *  * |  1  1  1  0  0 |  1  1  1 0
.   .   x   . |   2 |   * 192  * |  0  1  0  1  1 |  1  0  1 1
.   .   .   x |   2 |   *   * 96 |  0  0  2  0  2 |  0  1  2 1
--------------+-----+------------+----------------+-----------
x3/2o   .   . |   3 |   3   0  0 | 64  *  *  *  * |  1  1  0 0
x   .   x   . |   4 |   2   2  0 |  * 96  *  *  * |  1  0  1 0
x   .   .   x |   4 |   2   0  2 |  *  * 96  *  * |  0  1  1 0
.   o3/2x   . |   3 |   0   3  0 |  *  *  * 64  * |  1  0  0 1
.   .   x4/3x |   8 |   0   4  4 |  *  *  *  * 48 |  0  0  1 1
--------------+-----+------------+----------------+-----------
x3/2o3/2x   . ♦  12 |  12  12  0 |  4  6  0  4  0 | 16  *  * *
x3/2o   .   x ♦   6 |   6   0  3 |  2  0  3  0  0 |  * 32  * *
x   .   x4/3x ♦  16 |   8   8  8 |  0  4  4  0  2 |  *  * 24 *
.   o3/2x4/3x ♦  24 |   0  24 12 |  0  0  0  8  6 |  *  *  * 8