Small hecatonicosihecatonicosihecatonicosachoron

Small hecatonicosihecatonicosihecatonicosachoron
	(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Shiyay
Elements
Cells	120 small dodecicosahedra, 120 quasitruncated dodecadodecahedra, 120 great quasitruncated icosidodecahedra
Faces	3600 squares, 2400 hexagons, 1440 decagons, 1440 decagrams
Edges	3600+7200+7200
Vertices	7200
Vertex figure	Butterfly pyramid, base edge lengths √3, √(5+√5)/2, √3, √(5+√5)/2; lateral edge lengths √2, √2, √(5–√5)/2, √(5–√5)/2
Measures (edge length 1)
Circumradius
Dichoral angles	Siddy–10–quitdid: 108°
	Gaquatid–4–quitdid: 90°
	Siddy–6–gaquatid: 60°
	Gaquatid–10/3–quitdid: 36°
Related polytopes
Army	Semi-uniform Prahi
Regiment	Shipady
Conjugate	Great hecatonicosihecatonicosihecatonicosachoron
Abstract & topological properties
Euler characteristic	–2280
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small hecatonicosihecatonicosihecatonicosachoron, or shiyay, is a nonconvex uniform polychoron that consists of 120 small dodecicosahedra, 120 quasitruncated dodecadodecahedra, and 120 great quasitruncated icosidodecahedra. One small dodecicosahedron, two quasitruncated dodecadodecahedra, and two great quasitruncated icosidodecahedra join at each vertex.

Vertex coordinates[edit | edit source]

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