Acronym	gaqrin
Name	great quasirhombated penteract
Field of sections	©
Circumradius	sqrt[31-14 sqrt(2)]/2 = 1.673396
Vertex figure	©
Coordinates	((2 sqrt(2)-1)/2, (2 sqrt(2)-1)/2, (2 sqrt(2)-1)/2, (sqrt(2)-1)/2, 1/2)   & all permutations, all changes of sign
Face vector	640, 1600, 1520, 680, 122
Confer	general polytopal classes: Wythoffian polytera
External links

As abstract polyteron gaqrin is isomorph to girn, thereby replacing octagrams by octagons, resp. quitco by girco, resp. gaqrit by grit.

Incidence matrix according to Dynkin symbol

o3o3x3x4/3x

. . . .   . | 640 |   3   1   1 |   3   3   3  1 |   1   3   3  3 |  1  1  3
------------+-----+-------------+----------------+----------------+---------
. . x .   . |   2 | 960   *   * |   2   1   1  0 |   1   2   2  1 |  1  1  2
. . . x   . |   2 |   * 320   * |   0   3   0  1 |   0   3   0  3 |  1  0  3
. . . .   x |   2 |   *   * 320 |   0   0   3  1 |   0   0   3  3 |  0  1  3
------------+-----+-------------+----------------+----------------+---------
. o3x .   . |   3 |   3   0   0 | 640   *   *  * |   1   1   1  0 |  1  1  1
. . x3x   . |   6 |   3   3   0 |   * 320   *  * |   0   2   0  1 |  1  0  2
. . x .   x |   4 |   2   0   2 |   *   * 480  * |   0   0   2  1 |  0  1  2
. . . x4/3x |   8 |   0   4   4 |   *   *   * 80 |   0   0   0  3 |  0  0  3
------------+-----+-------------+----------------+----------------+---------
o3o3x .   . ♦   4 |   6   0   0 |   4   0   0  0 | 160   *   *  * |  1  1  0
. o3x3x   . ♦  12 |  12   6   0 |   4   4   0  0 |   * 160   *  * |  1  0  1
. o3x .   x ♦   6 |   6   0   3 |   2   0   3  0 |   *   * 320  * |  0  1  1
. . x3x4/3x ♦  48 |  24  24  24 |   0   8  12  6 |   *   *   * 40 |  0  0  2
------------+-----+-------------+----------------+----------------+---------
o3o3x3x   . ♦  20 |  30  10   0 |  20  10   0  0 |   5   5   0  0 | 32  *  *
o3o3x .   x ♦   8 |   6   0   4 |   8   0   6  0 |   2   0   4  0 |  * 80  *
. o3x3x4/3x ♦ 192 | 192  96  96 |  64  64  96 24 |   0  16  32  8 |  *  * 10