Spinoprismatodispentachoron

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

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.

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".