Hecatonicosihecatonicosihexacosichoron

Hecatonicosihecatonicosihexacosichoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Hihix
Elements
Cells	600 truncated tetrahedra, 120 tuncated great icosahedra, 120 small ditrigonal dodecicosidodecahedra
Faces	2400 triangles, 1440 pentagrams, 2400 hexagons, 720 decagons
Edges	3600+3600
Vertices	2400
Vertex figure	Inverted triangular antipodium, edge lengths (√5–1)/2 (top base), 1 (bottom base), √3 (side edges of triangles), and √(5+√5)/2 (side edges of crossed trapezoids)
Measures (edge length 1)
Circumradius	${\sqrt {\frac {13-3{\sqrt {5}}}{2}}}\approx 1.77367$
Hypervolume	$5{\frac {1022{\sqrt {5}}-2265}{4}}\approx 25.32684$
Dichoral angles	Tiggy–6–tut: $\arccos \left(-{\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 157.76124^{\circ }$
	Sidditdid–3–tut: $\arccos \left({\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 22.23876^{\circ }$
	Sidditdid–10–sidditdid: 72°
	Sidditdid–5/2–tiggy: 72°
Central density	81
Number of external pieces	188880
Level of complexity	686
Related polytopes
Army	Semi-uniform Sidpixhi
Regiment	Sadixady
Conjugate	Hexacosihecatonicosintercepted hecatonicosachoron
Abstract & topological properties
Euler characteristic	1320
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The hecatonicosihecatonicosihexacosichoron, or hihix, is a nonconvex uniform polychoron that consists of 120 truncated great icosahedra, 600 truncated tetrahedra, and 120 small ditrigonal dodecicosidodecahedra. Three truncated great icosahedra, three truncated tetrahedra, and three small ditrigonal dodecicosidodecahedra join at each vertex.

It also has 120 great stellated dodecahedra and 600 tetrahedra as pseudofacets.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small dishexacosidishecatonicosachoron.

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#472).