Acronym tox
Name truncated hexeract
Circumradius sqrt[(8+5 sqrt(2))/2] = 2.745093
Inradius
wrt. tan
[1+sqrt(2)]/2 = 1.207107
Inradius
wrt. hix
(5+3 sqrt(2))/sqrt(12) = 2.668121
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  
External
links
wikipedia   polytopewiki  

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

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