Acronym quacgarn
Name quasicelligreatorhombated penteract
Field of sections
` ©`
Circumradius sqrt[41-16 sqrt(2)]/2 = 2.143163
Vertex figure
` ©`
Coordinates ((3 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
Colonel of regiment (is itself locally convex – uniform polyteral members:
 by cells: cope gaqrit gaquidpoth ohope pittip prip quitcope tistodip quacgarn 80 10 0 0 0 32 40 80 gorcgrin 0 10 10 80 32 0 0 80
& others)
External

As abstract polytope quacgarn is isomorphic to cogrin, thereby replacing octagrams by octagons, resp. stop by op and quitco by girco, resp. tistodip by todip, quitcope by gircope, and gaqrit by grit.

Incidence matrix according to Dynkin symbol

```x3o3x3x4/3x

. . . .   . | 1920 |    2    2   1   1 |   1   2   2   2   1   2   2   1 |   1   1   1   2   2   2   1   1  2 |  1  1  1  2  1
------------+------+-------------------+---------------------------------+------------------------------------+---------------
x . . .   . |    2 | 1920    *   *   * |   1   1   1   1   0   0   0   0 |   1   1   1   1   1   1   0   0  0 |  1  1  1  1  0
. . x .   . |    2 |    * 1920   *   * |   0   1   0   0   1   1   1   0 |   1   0   0   1   1   0   1   1  1 |  1  1  0  1  1
. . . x   . |    2 |    *    * 960   * |   0   0   2   0   0   2   0   1 |   0   1   0   2   0   2   1   0  2 |  1  0  1  2  1
. . . .   x |    2 |    *    *   * 960 |   0   0   0   2   0   0   2   1 |   0   0   1   0   2   2   0   1  2 |  0  1  1  2  1
------------+------+-------------------+---------------------------------+------------------------------------+---------------
x3o . .   . |    3 |    3    0   0   0 | 640   *   *   *   *   *   *   * |   1   1   1   0   0   0   0   0  0 |  1  1  1  0  0
x . x .   . |    4 |    2    2   0   0 |   * 960   *   *   *   *   *   * |   1   0   0   1   1   0   0   0  0 |  1  1  0  1  0
x . . x   . |    4 |    2    0   2   0 |   *   * 960   *   *   *   *   * |   0   1   0   1   0   1   0   0  0 |  1  0  1  1  0
x . . .   x |    4 |    2    0   0   2 |   *   *   * 960   *   *   *   * |   0   0   1   0   1   1   0   0  0 |  0  1  1  1  0
. o3x .   . |    3 |    0    3   0   0 |   *   *   *   * 640   *   *   * |   1   0   0   0   0   0   1   1  0 |  1  1  0  0  1
. . x3x   . |    6 |    0    3   3   0 |   *   *   *   *   * 640   *   * |   0   0   0   1   0   0   1   0  1 |  1  0  0  1  1
. . x .   x |    4 |    0    2   0   2 |   *   *   *   *   *   * 960   * |   0   0   0   0   1   0   0   1  1 |  0  1  0  1  1
. . . x4/3x |    8 |    0    0   4   4 |   *   *   *   *   *   *   * 240 |   0   0   0   0   0   2   0   0  2 |  0  0  1  2  1
------------+------+-------------------+---------------------------------+------------------------------------+---------------
x3o3x .   . ♦   12 |   12   12   0   0 |   4   6   0   0   4   0   0   0 | 160   *   *   *   *   *   *   *  * |  1  1  0  0  0
x3o . x   . ♦    6 |    6    0   3   0 |   2   0   3   0   0   0   0   0 |   * 320   *   *   *   *   *   *  * |  1  0  1  0  0
x3o . .   x ♦    6 |    6    0   0   3 |   2   0   0   3   0   0   0   0 |   *   * 320   *   *   *   *   *  * |  0  1  1  0  0
x . x3x   . ♦   12 |    6    6   6   0 |   0   3   3   0   0   2   0   0 |   *   *   * 320   *   *   *   *  * |  1  0  0  1  0
x . x .   x ♦    8 |    4    4   0   4 |   0   2   0   2   0   0   2   0 |   *   *   *   * 480   *   *   *  * |  0  1  0  1  0
x . . x4/3x ♦   16 |    8    0   8   8 |   0   0   4   4   0   0   0   2 |   *   *   *   *   * 240   *   *  * |  0  0  1  1  0
. o3x3x   . ♦   12 |    0   12   6   0 |   0   0   0   0   4   4   0   0 |   *   *   *   *   *   * 160   *  * |  1  0  0  0  1
. o3x .   x ♦    6 |    0    6   0   3 |   0   0   0   0   2   0   3   0 |   *   *   *   *   *   *   * 320  * |  0  1  0  0  1
. . x3x4/3x ♦   48 |    0   24  24  24 |   0   0   0   0   0   8  12   6 |   *   *   *   *   *   *   *   * 80 |  0  0  0  1  1
------------+------+-------------------+---------------------------------+------------------------------------+---------------
x3o3x3x   . ♦   60 |   60   60  30   0 |  20  30  30   0  20  20   0   0 |   5  10   0  10   0   0   5   0  0 | 32  *  *  *  *
x3o3x .   x ♦   24 |   24   24   0  12 |   8  12   0  12   8   0  12   0 |   2   0   4   0   6   0   0   4  0 |  * 80  *  *  *
x3o . x4/3x ♦   24 |   24    0  12  12 |   8   0  12  12   0   0   0   3 |   0   4   4   0   0   3   0   0  0 |  *  * 80  *  *
x . x3x4/3x ♦   96 |   48   48  48  48 |   0  24  24  24   0  16  24  12 |   0   0   0   8  12   6   0   0  2 |  *  *  * 40  *
. o3x3x4/3x ♦  192 |    0  192  96  96 |   0   0   0   0  64  64  96  24 |   0   0   0   0   0   0  16  32  8 |  *  *  *  * 10
```

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