Acronym	caquapin
Name	celliquasiprismated penteract
Circumradius	sqrt[15-6 sqrt(2)]/2 = 1.276197
Coordinates	((2 sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
Colonel of regiment	getitdin
Face vector	640, 2240, 2880, 1520, 242
Confer	general polytopal classes: Wythoffian polytera
External links

As abstract polytope caquapin is isomorphic to cappin, thereby replacing quidpith by sidpith.

Incidence matrix according to Dynkin symbol

x3x3o3o4/3x

. . . .   . | 640 |   1   3   3 |   3   3   3   6   3 |   3   6   3   1   3   3  1 |  1  3  3  1  1
------------+-----+-------------+---------------------+----------------------------+---------------
x . . .   . |   2 | 320   *   * |   3   3   0   0   0 |   3   6   3   0   0   0  0 |  1  3  3  1  0
. x . .   . |   2 |   * 960   * |   1   0   2   2   0 |   2   2   0   1   2   1  0 |  1  2  1  0  1
. . . .   x |   2 |   *   * 960 |   0   1   0   2   2 |   0   2   2   0   1   2  1 |  0  1  2  1  1
------------+-----+-------------+---------------------+----------------------------+---------------
x3x . .   . |   6 |   3   3   0 | 320   *   *   *   * |   2   2   0   0   0   0  0 |  1  2  1  0  0
x . . .   x |   4 |   2   0   2 |   * 480   *   *   * |   0   2   2   0   0   0  0 |  0  1  2  1  0
. x3o .   . |   3 |   0   3   0 |   *   * 640   *   * |   1   0   0   1   1   0  0 |  1  1  0  0  1
. x . .   x |   4 |   0   2   2 |   *   *   * 960   * |   0   1   0   0   1   1  0 |  0  1  1  0  1
. . . o4/3x |   4 |   0   0   4 |   *   *   *   * 480 |   0   0   1   0   0   1  1 |  0  0  1  1  1
------------+-----+-------------+---------------------+----------------------------+---------------
x3x3o .   . ♦  12 |   6  12   0 |   4   0   4   0   0 | 160   *   *   *   *   *  * |  1  1  0  0  0
x3x . .   x ♦  12 |   6   6   6 |   2   3   0   3   0 |   * 320   *   *   *   *  * |  0  1  1  0  0
x . . o4/3x ♦   8 |   4   0   8 |   0   4   0   0   2 |   *   * 240   *   *   *  * |  0  0  1  1  0
. x3o3o   . ♦   4 |   0   6   0 |   0   0   4   0   0 |   *   *   * 160   *   *  * |  1  0  0  0  1
. x3o .   x ♦   6 |   0   6   3 |   0   0   2   3   0 |   *   *   *   * 320   *  * |  0  1  0  0  1
. x . o4/3x ♦   8 |   0   4   8 |   0   0   0   4   2 |   *   *   *   *   * 240  * |  0  0  1  0  1
. . o3o4/3x ♦   8 |   0   0  12 |   0   0   0   0   6 |   *   *   *   *   *   * 80 |  0  0  0  1  1
------------+-----+-------------+---------------------+----------------------------+---------------
x3x3o3o   . ♦  20 |  10  30   0 |  10   0  20   0   0 |   5   0   0   5   0   0  0 | 32  *  *  *  *
x3x3o .   x ♦  24 |  12  24  12 |   8   6   8  12   0 |   2   4   0   0   4   0  0 |  * 80  *  *  *
x3x . o4/3x ♦  24 |  12  12  24 |   4  12   0  12   6 |   0   4   3   0   0   3  0 |  *  * 80  *  *
x . o3o4/3x ♦  16 |   8   0  24 |   0  12   0   0  12 |   0   0   6   0   0   0  2 |  *  *  * 40  *
. x3o3o4/3x ♦  64 |   0  96  96 |   0   0  64  96  48 |   0   0   0  16  32  24  8 |  *  *  *  * 10