Acronym	prin
Name	prismatorhombated penteract, runcicantellated penteract
Field of sections	©
Circumradius	sqrt[23+10 sqrt(2)]/2 = 3.047217
Vertex figure	©   ©
Lace city in approx. ASCII-art	©   x3o4x u3o4x x3x4x x3x4x u3o4x x3o4x -- x3x3o4x (prit) u3o4x o3u4x o3u4x u3o4x -- o3u3o4x ((u,x)-srit) x3x4x o3u4x o3x4w o3x4w o3u4x x3x4x -- o3x3x4x (grit) x3x4x o3u4x o3x4w o3x4w o3u4x x3x4x -- o3x3x4x (grit) u3o4x o3u4x o3u4x u3o4x -- o3u3o4x ((u,x)-srit) x3o4x u3o4x x3x4x x3x4x u3o4x x3o4x -- x3x3o4x (prit)
Coordinates	((1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2)   & all permutations, all changes of sign
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – uniform polyteral members: by cells: deca grit prit sichado tisdip tuttip sibtadin 32 10 0 10 80 0 prin 32 0 10 0 80 80 & others)
Face vector	960, 2880, 2960, 1240, 202
Confer	related segmentotera: grittip   general polytopal classes: Wythoffian polytera   partial Stott expansions
External links

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

Incidence matrix according to Dynkin symbol

o3x3x3o4x

. . . . . | 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
. . . o4x |   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 . o4x ♦   8 |   4   0   8 |   0   0   4   0   0   2 |   *   *   *   * 240  * |  0  0  1  1
. . x3o4x ♦  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 . o4x ♦  12 |  12   0  12 |   4   0  12   0   0   3 |   0   4   0   0   3  0 |  *  * 80  *
. x3x3o4x ♦ 192 |  96 192 192 |   0  64  96  64  96  48 |   0   0  16  32  24  8 |  *  *  * 10

snubbed forms: o3x3x3o4s