Acronym	tox
Name	truncated hexeract
Circumradius	sqrt[(8+5 sqrt(2))/2] = 2.745093
Inradius wrt. hix	(5+3 sqrt(2))/sqrt(12) = 2.668121
Inradius wrt. tan	[1+sqrt(2)]/2 = 1.207107
Coordinates	((1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2)   & all permutations, all changes of sign
Volume	(8909+6300 sqrt(2))/90 = 197.983838
Surface	(7380+5214 sqrt(2)+2 sqrt(3))/15 = 983.811574
Dihedral angles (at margins)	at pen between hix and tan:   arccos[-1/sqrt(6)] = 114.094843° at tat between tan and tan:   90°
Face vector	384, 1152, 1520, 1120, 444, 76
Confer	general polytopal classes: Wythoffian polypeta   analogs: truncated hypercube tCn
External links

As abstract polytope tox is isomorphic to quotox, thereby replacing octagons by octagrams, resp. tic by quith, resp. tat by quitit, resp. tan by quittin.

Incidence matrix according to Dynkin symbol

o3o3o3o3x4x

. . . . . . | 384 |   5   1 |   10   5 |  10  10 |   5 10 |  1  5
------------+-----+---------+----------+---------+--------+------
. . . . x . |   2 | 960   * |    4   1 |   6   4 |   4  6 |  1  4
. . . . . x |   2 |   * 192 ♦    0   5 |   0  10 |   0 10 |  0  5
------------+-----+---------+----------+---------+--------+------
. . . o3x . |   3 |   3   0 | 1280   * |   3   1 |   3  3 |  1  3
. . . . x4x |   8 |   4   4 |    * 240 ♦   0   4 |   0  6 |  0  4
------------+-----+---------+----------+---------+--------+------
. . o3o3x . ♦   4 |   6   0 |    4   0 | 960   * |   2  1 |  1  2
. . . o3x4x ♦  24 |  24  12 |    8   6 |   * 160 |   0  3 |  0  3
------------+-----+---------+----------+---------+--------+------
. o3o3o3x . ♦   5 |  10   0 |   10   0 |   5   0 | 384  * |  1  1
. . o3o3x4x ♦  64 |  96  32 |   64  24 |  16   8 |   * 60 |  0  2
------------+-----+---------+----------+---------+--------+------
o3o3o3o3x . ♦   6 |  15   0 |   20   0 |  15   0 |   6  0 | 64  *
. o3o3o3x4x ♦ 160 | 320  80 |  320  80 | 160  40 |  32 10 |  * 12