Acronym	gacnet
Name	great cellated penteractitriacontiditeron, omnitruncated penteract, omnitruncated pentacross
Field of sections	©
Circumradius	sqrt[65+20 sqrt(2)]/2 = 4.829189
Inradius wrt. hodip	sqrt[57+18 sqrt(2)]/2 = 4.540260
Inradius wrt. tope	sqrt[(27+10 sqrt(2))/2] = 4.535534
Inradius wrt. gippid	sqrt[45+20 sqrt(2)]/2 = 4.280312
Inradius wrt. gircope	(7+sqrt(2))/2 = 4.207107
Inradius wrt. gidpith	sqrt[33+8 sqrt(2)]/2 = 3.328427
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
Volume	2[2053+1564 sqrt(2)] = 8529.660023
Dihedral angles	at toe between gippid and tope:   arccos[-2/sqrt(5)] = 153.434949° at hip between hodip and tope:   150° at op between gircope and hodip:   arccos[-sqrt(2/3)] = 144.735610° at hip between gippid and hodip:   arccos[-sqrt(3/5)] = 140.768480° at cube between gircope and tope:   135° at girco between gidpith and gircope:   135° at hip between gippid and gircope:   arccos[-sqrt(2/5)] = 129.231520° at op between gidpith and hodip:   arccos[-1/sqrt(3)] = 125.264390° at hip between gidpith and tope:   120° at toe between gidpith and gippid:   arccos[-1/sqrt(5)] = 116.565051°
Face vector	3840, 9600, 8160, 2640, 242
Confer	general polytopal classes: Wythoffian polytera   analogs: omnitruncated hypercube otCn
External links

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