Acronym quiprin Name quasiprismatorhombated penteract Circumradius sqrt[23-10 sqrt(2)]/2 = 1.488108 Vertex figure ` ©` Coordinates ((2 sqrt(2)-1)/2, (2 sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2, 1/2)   & all permutations, all changes of sign Colonel of regiment gibtadin Externallinks

As abstract polyteron quiprin is isomorph to prin, thereby replacing retrograde by prograde squares, resp. querco by sirco, resp. paqrit by prit.

Incidence matrix according to Dynkin symbol

```o3x3x3o4/3x

. . . .   . | 960 |   2   2   2 |   1   4   4   1   2   1 |   2   2   2   4   2  1 |  1  2  1  2
------------+-----+-------------+-------------------------+------------------------+------------
. x . .   . |   2 | 960   *   * |   1   2   2   0   0   0 |   2   2   1   2   1  0 |  1  2  1  1
. . x .   . |   2 |   * 960   * |   0   2   0   1   1   0 |   1   0   2   2   0  1 |  1  1  0  2
. . . .   x |   2 |   *   * 960 |   0   0   2   0   1   1 |   0   1   0   2   2  1 |  0  1  1  2
------------+-----+-------------+-------------------------+------------------------+------------
o3x . .   . |   3 |   3   0   0 | 320   *   *   *   *   * |   2   2   0   0   0  0 |  1  2  1  0
. x3x .   . |   6 |   3   3   0 |   * 640   *   *   *   * |   1   0   1   1   0  0 |  1  1  0  1
. x . .   x |   4 |   2   0   2 |   *   * 960   *   *   * |   0   1   0   1   1  0 |  0  1  1  1
. . x3o   . |   3 |   0   3   0 |   *   *   * 320   *   * |   0   0   2   0   0  1 |  1  0  0  2
. . x .   x |   4 |   0   2   2 |   *   *   *   * 480   * |   0   0   0   2   0  1 |  0  1  0  2
. . . o4/3x |   4 |   0   0   4 |   *   *   *   *   * 240 |   0   0   0   0   2  1 |  0  0  1  2
------------+-----+-------------+-------------------------+------------------------+------------
o3x3x .   . ♦  12 |  12   6   0 |   4   4   0   0   0   0 | 160   *   *   *   *  * |  1  1  0  0
o3x . .   x ♦   6 |   6   0   3 |   2   0   3   0   0   0 |   * 320   *   *   *  * |  0  1  1  0
. x3x3o   . ♦  12 |   6  12   0 |   0   4   0   4   0   0 |   *   * 160   *   *  * |  1  0  0  1
. x3x .   x ♦  12 |   6   6   6 |   0   2   3   0   3   0 |   *   *   * 320   *  * |  0  1  0  1
. x . o4/3x ♦   8 |   4   0   8 |   0   0   4   0   0   2 |   *   *   *   * 240  * |  0  0  1  1
. . x3o4/3x ♦  24 |   0  24  24 |   0   0   0   8  12   6 |   *   *   *   *   * 40 |  0  0  0  2
------------+-----+-------------+-------------------------+------------------------+------------
o3x3x3o   . ♦  30 |  30  30   0 |  10  20   0  10   0   0 |   5   0   5   0   0  0 | 32  *  *  *
o3x3x .   x ♦  24 |  24  12  12 |   8   8  12   0   6   0 |   2   4   0   4   0  0 |  * 80  *  *
o3x . o4/3x ♦  12 |  12   0  12 |   4   0  12   0   0   3 |   0   4   0   0   3  0 |  *  * 80  *
. x3x3o4/3x ♦ 192 |  96 192 192 |   0  64  96  64  96  48 |   0   0  16  32  24  8 |  *  *  * 10
```