Truncated icosahedral prism
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|Truncated icosahedral prism|
|Bowers style acronym||Tipe|
|Coxeter diagram||x o5x3x ()|
|Cells||12 pentagonal prisms, 20 hexagonal prisms, 2 truncated icosahedra|
|Faces||30+60 squares, 24 pentagons, 40 hexagons|
|Vertex figure||Sphenoid, edge lengths (1+√5)/2, √3, √3 (base), √2 (legs)|
|Measures (edge length 1)|
|Number of pieces||34|
|Level of complexity||12|
|Dual||Pentakis dodecahedral tegum|
|Conjugate||Truncated great icosahedral prism|
|Symmetry||H3×A1, order 240|
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).
Gallery[edit | edit source]
Segmentochoron display, ti atop ti
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".