Acronym tox Name truncated hexeract Circumradius sqrt[(8+5 sqrt(2))/2] = 2.745093 Inradiuswrt. hix (5+3 sqrt(2))/sqrt(12) = 2.668121 Inradiuswrt. 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° Confer analogs: truncated hypercube tCn Externallinks

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
```