Prismatopentahemidecachoron

Prismatopentahemidecachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Piphid
Coxeter diagram
Elements
Cells	5 tetrahedra, 10 triangular prisms, 5 cuboctahedra
Faces	20+20 triangles, 30 squares
Edges	30+30
Vertices	20
Vertex figure	Triangular cuploid, edge lengths 1 (top triangle and based pseudo-triangle) and √2 (sides)
Measures (edge length 1)
Circumradius	1
Dichoral angles	Tet–3–co: $\arccos\left(\frac14\right) ≈ 75.52249°$
	Co–4–trip: $\arccos\left(\frac{\sqrt6}{6}\right) ≈ 65.90516°$
	Co–3–trip: $\arccos\left(\frac{\sqrt6}{4}\right) ≈ 52.23876°$
Number of external pieces	85
Level of complexity	20
Related polytopes
Army	Spid
Regiment	Spid
Conjugate	None
Abstract & topological properties
Euler characteristic	10
Orientable	No
Properties
Symmetry	A4, order 120
Convex	No
Nature	Tame

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

It also has 5 tetrahedra and 10 triangular prisms as pseudofacets.

Gallery

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 11: Antipodiumverts" (#443).

• Klitzing, Richard. "piphid".