P*
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P*  

Rank  3 
Type  Quasiconvex Stewart toroid 
Elements  
Faces  20+60+60+60 triangles, 60 squares 
Edges  30+30+60+60+120+120 
Vertices  20+60+60 
Measures (edge length 1)  
Volume  
Surface area  
Related polytopes  
Convex hull  Truncated dodecahedron 
Abstract & topological properties  
Flag count  1680 
Euler characteristic  –20 
Orientable  Yes 
Genus  11 
Properties  
Symmetry  H_{3}, order 120 
Flag orbits  14 
Convex  No 
P* is a quasiconvex Stewart toroid in the T_{5} 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 pseudofaces, its faces are all triangles or squares.
Vertex coordinates[edit  edit source]
This April 2024 is missing vertex coordinates. 
Gallery[edit  edit source]

The view from the inside

A view where the external faces are transparent, making the internal tunnel structure more apparent.

A cutaway view. The grey pentagons are pseudofaces of the original polyhedron.
Related polytopes[edit  edit source]
A subset of the vertices and edges of P* form those of P''.
External links[edit  edit source]
 Webb, Robert. "Drilled truncated dodecahedron".
 Doskey, Alex. "Chapter 15  Expedition into 'T_{5}Country' ".
Bibliography[edit  edit source]
 Stewart, Bonnie (1964). Adventures Amoung the Toroids (2 ed.). ISBN 0686119 363.