Truncated icosahedral prism
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Truncated icosahedral prism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Tipe 
Coxeter diagram  x o5x3x () 
Elements  
Cells  12 pentagonal prisms, 20 hexagonal prisms, 2 truncated icosahedra 
Faces  30+60 squares, 24 pentagons, 40 hexagons 
Edges  60+60+120 
Vertices  120 
Vertex figure  Sphenoid, edge lengths (1+√5)/2, √3, √3 (base), √2 (legs) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Pip–4–hip: 
Hip–4–hip:  
Ti–5–pip: 90°  
Ti–6–hip: 90°  
Height  1 
Central density  1 
Number of external pieces  34 
Level of complexity  12 
Related polytopes  
Army  Tipe 
Regiment  Tipe 
Dual  Pentakis dodecahedral tegum 
Conjugate  Truncated great icosahedral prism 
Abstract & topological properties  
Flag count  2880 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  H_{3}×A_{1}, order 240 
Convex  Yes 
Nature  Tame 
The truncated icosahedral prism or tipe is a prismatic uniform polychoron that consists of 2 truncated icosahedra, 12 pentagonal prisms, and 20 hexagonal prisms. Each vertex joins 1 truncated icosahedron, 1 pentagonal prism, and 2 hexagonal prisms. It is a prism based on the truncated icosahedron. As such it is also a CRF segmentochoron (designated K4.127 on Richard Klitzing's list).
Gallery[edit  edit source]

Segmentochoron display, ti atop ti

Net
Vertex coordinates[edit  edit source]
Coordinates for the vertices of a truncated icosahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:
Representations[edit  edit source]
A truncated icosahedral prism has the following Coxeter diagrams:
 x o5x3x (full symmetry)
 oo5xx3xx&#x (bases considered separately)
External links[edit  edit source]
 Bowers, Jonathan. "Category 19: Prisms" (#902).
 Klitzing, Richard. "Tipe".
 Wikipedia contributors. "Truncated icosahedral prism".