Acronym gacnet Name great cellated penteractitriacontiditeron,omnitruncated penteract,omnitruncated pentacross Field of sections ` ©` Circumradius sqrt[65+20 sqrt(2)]/2 = 4.829189 Vertex figure ` ©   ©` Coordinates ((1+4 sqrt(2))/2, (1+3 sqrt(2))/2, (1+2 sqrt(2))/2, (1+sqrt(2))/2, 1/2)   & all permutations, all changes of sign Externallinks

As abstract polytope gacnet is isomorphic to gaquacint, thereby replacing octagons by octagrams, resp. op by stop and girco by quitco, resp. hodip by histodip, gircope by quitcope, and gidpith by gaquidpoth.

Incidence matrix according to Dynkin symbol

```x3x3x3x4x

. . . . . | 3840 |    1    1    1    1    1 |   1   1   1   1   1   1   1   1   1   1 |   1   1   1   1   1   1   1   1   1  1 |  1  1  1  1  1
----------+------+--------------------------+-----------------------------------------+----------------------------------------+---------------
x . . . . |    2 | 1920    *    *    *    * |   1   1   1   1   0   0   0   0   0   0 |   1   1   1   1   1   1   0   0   0  0 |  1  1  1  1  0
. x . . . |    2 |    * 1920    *    *    * |   1   0   0   0   1   1   1   0   0   0 |   1   1   1   0   0   0   1   1   1  0 |  1  1  1  0  1
. . x . . |    2 |    *    * 1920    *    * |   0   1   0   0   1   0   0   1   1   0 |   1   0   0   1   1   0   1   1   0  1 |  1  1  0  1  1
. . . x . |    2 |    *    *    * 1920    * |   0   0   1   0   0   1   0   1   0   1 |   0   1   0   1   0   1   1   0   1  1 |  1  0  1  1  1
. . . . x |    2 |    *    *    *    * 1920 |   0   0   0   1   0   0   1   0   1   1 |   0   0   1   0   1   1   0   1   1  1 |  0  1  1  1  1
----------+------+--------------------------+-----------------------------------------+----------------------------------------+---------------
x3x . . . |    6 |    3    3    0    0    0 | 640   *   *   *   *   *   *   *   *   * |   1   1   1   0   0   0   0   0   0  0 |  1  1  1  0  0
x . x . . |    4 |    2    0    2    0    0 |   * 960   *   *   *   *   *   *   *   * |   1   0   0   1   1   0   0   0   0  0 |  1  1  0  1  0
x . . x . |    4 |    2    0    0    2    0 |   *   * 960   *   *   *   *   *   *   * |   0   1   0   1   0   1   0   0   0  0 |  1  0  1  1  0
x . . . x |    4 |    2    0    0    0    2 |   *   *   * 960   *   *   *   *   *   * |   0   0   1   0   1   1   0   0   0  0 |  0  1  1  1  0
. x3x . . |    6 |    0    3    3    0    0 |   *   *   *   * 640   *   *   *   *   * |   1   0   0   0   0   0   1   1   0  0 |  1  1  0  0  1
. x . x . |    4 |    0    2    0    2    0 |   *   *   *   *   * 960   *   *   *   * |   0   1   0   0   0   0   1   0   1  0 |  1  0  1  0  1
. x . . x |    4 |    0    2    0    0    2 |   *   *   *   *   *   * 960   *   *   * |   0   0   1   0   0   0   0   1   1  0 |  0  1  1  0  1
. . x3x . |    6 |    0    0    3    3    0 |   *   *   *   *   *   *   * 640   *   * |   0   0   0   1   0   0   1   0   0  1 |  1  0  0  1  1
. . x . x |    4 |    0    0    2    0    2 |   *   *   *   *   *   *   *   * 960   * |   0   0   0   0   1   0   0   1   0  1 |  0  1  0  1  1
. . . x4x |    8 |    0    0    0    4    4 |   *   *   *   *   *   *   *   *   * 480 |   0   0   0   0   0   1   0   0   1  1 |  0  0  1  1  1
----------+------+--------------------------+-----------------------------------------+----------------------------------------+---------------
x3x3x . . ♦   24 |   12   12   12    0    0 |   4   6   0   0   4   0   0   0   0   0 | 160   *   *   *   *   *   *   *   *  * |  1  1  0  0  0
x3x . x . ♦   12 |    6    6    0    6    0 |   2   0   3   0   0   3   0   0   0   0 |   * 320   *   *   *   *   *   *   *  * |  1  0  1  0  0
x3x . . x ♦   12 |    6    6    0    0    6 |   2   0   0   3   0   0   3   0   0   0 |   *   * 320   *   *   *   *   *   *  * |  0  1  1  0  0
x . x3x . ♦   12 |    6    0    6    6    0 |   0   3   3   0   0   0   0   2   0   0 |   *   *   * 320   *   *   *   *   *  * |  1  0  0  1  0
x . x . x ♦    8 |    4    0    4    0    4 |   0   2   0   2   0   0   0   0   2   0 |   *   *   *   * 480   *   *   *   *  * |  0  1  0  1  0
x . . x4x ♦   16 |    8    0    0    8    8 |   0   0   4   4   0   0   0   0   0   2 |   *   *   *   *   * 240   *   *   *  * |  0  0  1  1  0
. x3x3x . ♦   24 |    0   12   12   12    0 |   0   0   0   0   4   6   0   4   0   0 |   *   *   *   *   *   * 160   *   *  * |  1  0  0  0  1
. x3x . x ♦   12 |    0    6    6    0    6 |   0   0   0   0   2   0   3   0   3   0 |   *   *   *   *   *   *   * 320   *  * |  0  1  0  0  1
. x . x4x ♦   16 |    0    8    0    8    8 |   0   0   0   0   0   4   4   0   0   2 |   *   *   *   *   *   *   *   * 240  * |  0  0  1  0  1
. . x3x4x ♦   48 |    0    0   24   24   24 |   0   0   0   0   0   0   0   8  12   6 |   *   *   *   *   *   *   *   *   * 80 |  0  0  0  1  1
----------+------+--------------------------+-----------------------------------------+----------------------------------------+---------------
x3x3x3x . ♦  120 |   60   60   60   60    0 |  20  30  30   0  20  30   0  20   0   0 |   5  10   0  10   0   0   5   0   0  0 | 32  *  *  *  *
x3x3x . x ♦   48 |   24   24   24    0   24 |   8  12   0  12   8   0  12   0  12   0 |   2   0   4   0   6   0   0   4   0  0 |  * 80  *  *  *
x3x . x4x ♦   48 |   24   24    0   24   24 |   8   0  12  12   0  12  12   0   0   6 |   0   4   4   0   0   3   0   0   3  0 |  *  * 80  *  *
x . x3x4x ♦   96 |   48    0   48   48   48 |   0  24  24  24   0   0   0  16  24  12 |   0   0   0   8  12   6   0   0   0  2 |  *  *  * 40  *
. x3x3x4x ♦  384 |    0  192  192  192  192 |   0   0   0   0  64  96  96  64  96  48 |   0   0   0   0   0   0  16  32  24  8 |  *  *  *  * 10

snubbed forms: x3x3x3x4s, s3s3s3s4x, s3s3s3s4s
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