Small hexacosihecatonicosihecatonicosachoron

Small hexacosihecatonicosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sixhihy
Coxeter diagram	o3o3/2x5x5*b ()
Elements
Cells	600 tetrahedra, 120 dodecahedra, 120 small dodecicosidodecahedra
Faces	2400 triangles, 1440 pentagons, 720 decagons
Edges	3600+3600
Vertices	2400
Vertex figure	Crossed triangular frustum, edge lengths 1 (small base), (1+√5)/2 (large base), and √(5+√5)/2 (sides)
Measures (edge length 1)
Circumradius	$3+{\sqrt {5}}\approx 5.23607$
Hypervolume	$5{\frac {3665+1622{\sqrt {5}}}{4}}\approx 9114.87782$
Dichoral angles	Saddid–10–saddid: 144°
	Saddid–5–doe: 144°
	Saddid–3–tet: $\arccos \left({\frac {\sqrt {7+3{\sqrt {5}}}}{4}}\right)\approx 22.23876^{\circ }$
Number of external pieces	4560
Level of complexity	12
Related polytopes
Army	Sidpixhi
Regiment	Sidpixhi
Conjugate	Great hexacosihecatonicosihecatonicosachoron
Abstract & topological properties
Flag count	86400
Euler characteristic	–1080
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small hexacosihecatonicosihecatonicosachoron, or sixhihy, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra, 120 regular dodecahedra, and 120 small dodecicosidodecahedra. 1 tetrahedron, 1 dodecahedron, and 3 small dodecicosidodecahedra join at each vertex.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#457).

• Klitzing, Richard. "sixhihy".