P*

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P*
Rank3
TypeQuasi-convex Stewart toroid
Elements
Faces20+60+60+60 triangles, 60 squares
Edges30+30+60+60+120+120
Vertices20+60+60
Measures (edge length 1)
Volume
Surface area
Related polytopes
Convex hullTruncated dodecahedron
Abstract & topological properties
Flag count1680
Euler characteristic–20
OrientableYes
Genus11
Properties
SymmetryH3, order 120
Flag orbits14
ConvexNo

P* is a quasi-convex Stewart toroid in the T5 country.

It can be made by excavating 12 pentagonal cupolae, 12 pentagonal antiprisms and 1 dodecahedron from a truncated dodecahedron, or as the outer blend of 1 P'', 2 oriental hats, and 10 Cs.

Although it has pentagons, decagons, and 36°-144° rhombi as pseudo-faces, its faces are all triangles or squares.

Vertex coordinates[edit | edit source]

Gallery[edit | edit source]

Related polytopes[edit | edit source]

A subset of the vertices and edges of P* form those of P''.

External links[edit | edit source]

Bibliography[edit | edit source]

  • Stewart, Bonnie (1964). Adventures Amoung the Toroids (2 ed.). ISBN 0686-119 36-3.