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
External
links
hedrondude   wikipedia  

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

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