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 Externallinks

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
```