Acronym	dox (old: gex)
Name	dodecahedronary hexacosachoron (great hexacosachoron), compound of 25 ico
Coxeter symbol	5{3,3,5}[25{3,4,3}]{3,3,5}
Circumradius	1
Inradius	1/sqrt(2) = 0.707107
Coordinates	(1, 0, 0, 0)                                         & all permutations, all changes of sign (vertex inscribed q-hex) (1/2, 1/2, 1/2, 1/2)                             & all permutations, all changes of sign (vertex inscribed tes) ((1+sqrt(5))/4, (sqrt(5)-1)/4, 1/4, 0)   & all even permutations, all changes of sign (vertex inscribed v-sadi)
General of army	ex
Colonel of regiment	sishi
Captain of company	sidtixhi
Admiral of fleet	ex
Confer	related compounds: chi   Grünbaumian relatives: dittady+dox   gidtixhi+dox   sidtixhi+dox   general polytopal classes: regular
External links

Dox occurs in 2 different forms depending on whether the vertices (coincident by 5) will be counted separately (type A), or will be identified (type B).

Dox also can be seen as a compound of 5 chi, again either counting the incident vertices separately (type C), or identifying them (type D).

Incidence matrix

(Type A)

 600 ♦    8 |   12 |   6 ||  1
-----+------+------+-----++---
   2 | 2400 |    3 |   3 ||  1
-----+------+------+-----++---
   3 |    3 | 2400 |   2 ||  1
-----+------+------+-----++---
♦  6 |   12 |    8 | 600 ||  1
-----+------+------+-----++---
♦ 24 |   96 |   96 |  24 || 25

(Type B)

 120 ♦   40 |   60 |  30 ||  5
-----+------+------+-----++---
   2 | 2400 |    3 |   3 ||  1
-----+------+------+-----++---
   3 |    3 | 2400 |   2 ||  1
-----+------+------+-----++---
♦  6 |   12 |    8 | 600 ||  1
-----+------+------+-----++---
♦ 24 |   96 |   96 |  24 || 25

(Type C)

  600 ♦    8 |   12 |   6 || 1
------+------+------+-----++--
    2 | 2400 |    3 |   3 || 1
------+------+------+-----++--
    3 |    3 | 2400 |   2 || 1
------+------+------+-----++--
♦   6 |   12 |    8 | 600 || 1
------+------+------+-----++--
♦ 120 |  480 |  480 | 120 || 5

(Type D)

  120 ♦   40 |   60 |  30 || 5
------+------+------+-----++--
    2 | 2400 |    3 |   3 || 1
------+------+------+-----++--
    3 |    3 | 2400 |   2 || 1
------+------+------+-----++--
♦   6 |   12 |    8 | 600 || 1
------+------+------+-----++--
♦ 120 |  480 |  480 | 120 || 5