Acronym	girn
Name	great rhombated penteract, cantitruncated penteract
Field of sections	©
Circumradius	sqrt[31+14 sqrt(2)]/2 = 3.563671
Vertex figure	©   ©
Coordinates	((1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/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 girn is isomorph to gaqrin, thereby replacing octagons by octagrams, resp. girco by quitco, resp. grit by gaqrit.

Incidence matrix according to Dynkin symbol

o3o3x3x4x

. . . . . | 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
. . . x4x |   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
. . x3x4x ♦  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  *
. o3x3x4x ♦ 192 | 192  96  96 |  64  64  96 24 |   0  16  32  8 |  *  * 10

snubbed forms: o3o3x3x4s