Prismatopentahemidecachoron

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Prismatopentahemidecachoron
Rank4
TypeUniform
Notation
Bowers style acronymPiphid
Coxeter diagram
Elements
Cells5 tetrahedra, 10 triangular prisms, 5 cuboctahedra
Faces20+20 triangles, 30 squares
Edges30+30
Vertices20
Vertex figureTriangular cuploid, edge lengths 1 (top triangle and based pseudo-triangle) and 2 (sides)
Measures (edge length 1)
Circumradius1
Dichoral anglesTet–3–co:
 Co–4–trip:
 Co–3–trip:
Number of external pieces85
Level of complexity20
Related polytopes
ArmySpid
RegimentSpid
ConjugateNone
Abstract & topological properties
Flag count960
Euler characteristic10
OrientableNo
Properties
SymmetryA4, order 120
ConvexNo
NatureTame

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[edit | edit source]

Vertex coordinates[edit | edit source]

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

External links[edit | edit source]