Antifrustary hexacositrishecatonicosachoron

Antifrustary hexacositrishecatonicosachoron
	(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Affixthi
Coxeter diagram	x3o5x5/2o3a5/3c
Elements
Cells	600 octahedra, 120 dodecadodecahedra, 120 great dodecicosidodecahedra, 120 great ditrigonal dodecicosidodecahedra
Faces	2400+2400 triangles, 1440 pentagons, 1440 pentagrams, 1440 decagrams
Edges	7200+7200
Vertices	3600
Vertex figure	Rectangular frustum, edge lengths 1 (top square), (1+√5)/2 and (√5–1)/2 (base rectangle), and √(5–√5)/2 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Oct–3–gaddid:
	Did–5/2–gaddid: 144°
	Did–5–gidditdid: 144°
	Gaddid–10/3–gidditdid: 144°
	Oct–3–gidditdid:
Number of external pieces	12720
Related polytopes
Army	Semi-uniform Xhi
Regiment	Affixthi
Conjugate	Retrofrustary hexacositrishecatonicosachoron
Abstract & topological properties
Euler characteristic	–2640
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The antifrustary hexacositrishecatonicosachoron, or affixthi, is a nonconvex uniform polychoron that consists of 600 octahedra, 120 dodecadodecahedra, 120 great dodecicosidodecahedra, and 120 great ditrigonal dodecicosidodecahedra. 1 octahedron, 1 dodecadodecahedron, 2 great dodecicosidodecahedra, and 2 great ditrigonal dodecicosidodecahedra join at each vertex.

The antifrustary hexacositrishecatonicosachoron contains the vertices of a great prismatodecachoron.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

Coordinates for the vertices of an antifrustary hexacositrishecatonicosachoron of edge length 1 are given by all permutations of:

$\left(0,\,0,\,±1,\,±2\right),$
$\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac{2+\sqrt5}{2}\right),$
$\left(±1,\,±1,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2}\right),$
$\left(±\frac12,\,±\frac12,\,±\frac32,\,±\frac32\right),$
$\left(±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac12,\,±\frac32\right),$

together with all even permutations of:

$\left(0,\,±\frac{\sqrt5-2}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$
$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{2+\sqrt5}{2}\right),$
$\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac{\sqrt5}{2}\right),$
$\left(0,\,±\frac{\sqrt5}{2},\,±\frac{3\sqrt5-1}{4},\,±\frac{3+\sqrt5}{4}\right),$
$\left(±\frac{\sqrt5-2}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),$
$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{2+\sqrt5}{2}\right),$
$\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac32\right),$
$\left(±\frac{3-\sqrt5}{4},\,±\frac12,\,±\frac{1+3\sqrt5}{4},\,±1\right),$
$\left(±\frac{3-\sqrt5}{4},\,±1,\,±\frac32,\,±\frac{3+\sqrt5}{4}\right),$
$\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac{1+\sqrt5}{2},\,±\frac{3\sqrt5-1}{4}\right),$
$\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±2,\,±\frac{1+\sqrt5}{4}\right),$
$\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{5+\sqrt5}{4},\,±\frac{\sqrt5}{2}\right),$
$\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{1+3\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\right),$
$\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{5+\sqrt5}{4},\,±1\right),$
$\left(±\frac12,\,±1,\,±\frac{3+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4}\right),$
$\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac32\right),$
$\left(±\frac{5-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{\sqrt5}{2},\,±\frac{1+\sqrt5}{2}\right).$