Small rhombiprismic hecatonicosihecatonicosachoron

Small rhombiprismic hecatonicosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Sirphihy
Elements
Cells	720 decagonal prisms, 120 rhombicosahedra, 120 great rhombicosidodecahedra
Faces	3600+3600 squares, 2400 hexagons, 1440 decagons
Edges	3600+7200+7200
Vertices	7200
Vertex figure	Butterfly pyramid, base edge lengths √2, √3, √2, √3; lateral edge lengths √2, √2, √(5+√5)/2, √(5+√5)/2
Measures (edge length 1)
Circumradius	${\sqrt {13+5{\sqrt {5}}}}\approx 4.91735$
Dichoral angles	Ri–4–dip: $\arccos \left(-{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 148.28253^{\circ }$
	Grid–4–dip: $\arccos \left(-{\sqrt {\frac {5-{\sqrt {5}}}{10}}}\right)\approx 121.71747^{\circ }$
	Ri–6–grid: 120°
	Grid–10–dip: 18°
Related polytopes
Army	Semi-uniform Grix, edge lengths ${\frac {{\sqrt {5}}-1}{2}}$ (pentagonal prisms), ${\frac {3-{\sqrt {5}}}{2}}$ (remaining edges)
Regiment	Pirghi
Conjugate	Great rhombiprismic hecatonicosihecatonicosachoron
Abstract & topological properties
Flag count	230400
Euler characteristic	–720
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small rhombiprismic hecatonicosihecatonicosachoron, or sirphihy, is a nonconvex uniform polychoron that consists of 120 rhombicosahedra, 720 decagonal prisms, and 120 great rhombicosidodecahedra. One rhombicosahedron, two decagonal prisms, and two great rhombicosidodecahedra join at each vertex.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the prismatorhombated great hecatonicosachoron.

External links

• Bowers, Jonathan. "Category 10: Prismatorhombates" (#375).