Spinoprismatodispentachoron

The spinoprismatodispentachoron, or nipdip, is a nonconvex uniform polychoron that consists of 5 tetrahedra, 10 triangular prisms, and 5 cubohemioctahedra. One tetrahedron, three triangular prisms, and three cubohemioctahedra join at each vertex.

Spinoprismatodispentachoron
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Nipdip
Elements
Cells	5 tetrahedra, 10 triangular prisms, 5 cubohemioctahedra
Faces	20 triangles, 30 squares, 10 hexagons
Edges	30+30
Vertices	20
Vertex figure	Triangular crown, edge lengths 1 (top triangle), √2 (side edges of triangles), and √3 (edges joining butterflies)
Measures (edge length 1)
Circumradius	1
Dichoral angles	Tet–3–trip: $\arccos \left(-{\frac {\sqrt {6}}{4}}\right)\approx 127.76124^{\circ }$
	Cho–6–cho: $\arccos \left({\frac {1}{4}}\right)\approx 75.52249^{\circ }$
	Cho–4–trip: $\arccos \left({\frac {\sqrt {6}}{6}}\right)\approx 65.90516^{\circ }$
Number of external pieces	45
Level of complexity	12
Related polytopes
Army	Spid
Regiment	Spid
Conjugate	None
Abstract & topological properties
Flag count	960
Euler characteristic	0
Orientable	No
Properties
Symmetry	A4, order 120
Convex	No
Nature	Wild

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#446).

• Klitzing, Richard. "nipdip".