|Bowers style acronym||Iddip|
|Coxeter diagram||x o5x3o ()|
|Cells||20 triangular prisms, 12 pentagonal prisms, 2 icosidodecahedra|
|Faces||40 triangles, 60 squares, 24 pentagons|
|Vertex figure||Rectangular pyramid, edge lengths 1, (1+√5)/2 (base), √2 (legs)|
|Measures (edge length 1)|
|Number of external pieces||34|
|Level of complexity||8|
|Dual||Rhombic triacontahedral tegum|
|Conjugate||Great icosidodecahedral prism|
|Abstract & topological properties|
|Symmetry||H3×A1, order 240|
The icosidodecahedral prism or iddip, is a prismatic uniform polychoron that consists of 2 icosidodecahedra, 12 pentagonal prisms, and 20 triangular prisms. Each vertex joins 1 icosidodecahedron, 2 pentagonal prisms, and 2 triangular prisms. It is a prism based on the icosidodecahedron. As such it is also a convex segmentochoron (designated K-4.90 on Richard Klitzing's list).
Gallery[edit | edit source]
Card with cell counts, verf, and cross-sections
Segmentochoron display, id atop id
Vertex coordinates[edit | edit source]
The vertices of an icosidodecahedral prism of edge length 1 are given by all permutations and sign changes of the first three coordinates of:
along with all even permutations and all sign changes of the first three coordinates of:
Representations[edit | edit source]
An icosidodecahedral prism has the following Coxeter diagrams:
- x o5x3o (full symmetry)
- oo5xx3oo&#x (bases seen separately)
- xxxxx xoxfo5ofxox&#xt (H2×A1 axial, pentagonal prism-first)
Related polychora[edit | edit source]
The regiment of the icosidodecahedral prism also includes the small icosihemidodecahedral prism and small dodecahemidodecahedral prism.
External links[edit | edit source]
- Bowers, Jonathan. "Category 19: Prisms" (#911).
- Klitzing, Richard. "Iddip".
- Wikipedia Contributors. "Icosidodecahedral prism".