Truncated icosahedral prism

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 K-4.127 on Richard Klitzing's list).

Truncated icosahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymTipe
Coxeter diagramx o5x3x ()
Elements
Cells12 pentagonal prisms, 20 hexagonal prisms, 2 truncated icosahedra
Faces30+60 squares, 24 pentagons, 40 hexagons
Edges60+60+120
Vertices120
Vertex figureSphenoid, edge lengths (1+5)/2, 3, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesPip–4–hip:
 Hip–4–hip:
 Ti–5–pip: 90°
 Ti–6–hip: 90°
Height1
Central density1
Number of external pieces34
Level of complexity12
Related polytopes
ArmyTipe
RegimentTipe
DualPentakis dodecahedral tegum
ConjugateTruncated great icosahedral prism
Abstract & topological properties
Flag count2880
Euler characteristic0
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexYes
NatureTame

Gallery edit

Vertex coordinates edit

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

A truncated icosahedral prism has the following Coxeter diagrams:

  • x o5x3x (full symmetry)
  • oo5xx3xx&#x (bases considered separately)

External links edit