Small spinoprismatohecatonicosihecatonicosachoron

Small spinoprismatohecatonicosihecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Snaphihy
Elements
Cells	720 pentagrammic prisms, 120 great stellated dodecahedra, 120 rhombicosahedra
Faces	3600 squares, 1440 pentagrams, 1200 hexagons
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular crown, edge lengths (√5–1)/2 (top triangle), √2 (side edges of triangles), and √3 (edges between butterflies)
Measures (edge length 1)
Circumradius	2
Dichoral angles	Gissid–5/2–stip: 162°
	Ri–4–stip: $\arccos \left(-{\sqrt {\frac {5+{\sqrt {5}}}{10}}}\right)\approx 148.28253^{\circ }$
	Ri–6–ri: 120°
Number of external pieces	50040
Level of complexity	144
Related polytopes
Army	Sidpixhi
Regiment	Siddapady
Conjugate	Great spinoprismatohecatonicosihecatonicosachoron
Abstract & topological properties
Euler characteristic	480
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Wild

The small spinoprismatohecatonicosihecatonicosachoron, or snaphihy, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra, 720 pentagrammic prisms, and 120 rhombicosahedra. One great stellated dodecahedron, three pentagrammic prisms, and three rhombicosahedra join at each vertex.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#466).