|Bowers style acronym||Ipe|
|Coxeter diagram||x o5o3x ()|
|Cells||20 triangular prisms, 2 icosahedra|
|Faces||40 triangles, 30 squares|
|Vertex figure||Pentagonal pyramid, edge lengths 1 (base), √2 (legs)|
|Measures (edge length 1)|
|Number of external pieces||22|
|Level of complexity||4|
|Conjugate||Great icosahedral prism|
|Abstract & topological properties|
|Symmetry||H3×A1, order 240|
The icosahedral prism or ipe is a prismatic uniform polychoron that consists of 2 icosahedra and 20 triangular prisms. Each vertex joins 1 icosahedron and 5 triangular prisms. It is a prism based on the icosahedron. As such it is also a convex segmentochoron (designated K-4.36 in Richard Klitzing's list).
Gallery[edit | edit source]
Card with cell counts, verf, and cross-sections
Segmentochoron display, ike atop ike
Vertex coordinates[edit | edit source]
The vertices of an icosahedral prism of edge length 1 are given by all even permutations and all sign changes of the first three coordinates of:
Representations[edit | edit source]
An icosahedral prism has the following Coxeter diagrams:
- x o5o3x (full symmetry)
- x2s3s4o () (bases as pyritohedral symmetry)
- x2s3s3s () (as snub tetrahedral prism)
- oo5oo3xx&#x (bases seen separately)
- xxxx oxoo5ooxo&#xt (H2×A1 axial, edge-first)
Related polychora[edit | edit source]
An icosahedral prism can be cut into a central pentagonal antiprismatic prism augmented with 2 pentagonal pyramidal prisms.
The regiment of the icosahedral prism also contains the great dodecahedral prism.
External links[edit | edit source]
- Bowers, Jonathan. "Category 19: Prisms" (#892).
- Klitzing, Richard. "Ipe".
- Wikipedia Contributors. "Icosahedral prism".