The dodecahedral prism or dope is a prismatic uniform polychoron that consists of 2 dodecahedra and 12 pentagonal prisms. Each vertex joins 1 dodecahedron and 3 pentagonal prisms. It is a prism based on the dodecahedron. As such it is also a convex segmentochoron (designated K-4.74 on Richard Klitzing's list).
|Bowers style acronym||Dope|
|Coxeter diagram||x x5o3o ()|
|Cells||12 pentagonal prisms, 2 dodecahedra|
|Faces||30 squares, 24 pentagons|
|Vertex figure||Triangular pyramid, edge lengths (1+√5)/2 (base), √2 (legs)|
|Measures (edge length 1)|
|Number of external pieces||14|
|Level of complexity||4|
|Conjugate||Great stellated dodecahedral prism|
|Abstract & topological properties|
|Symmetry||H3×A1, order 240|
Card with cell counts, verf, and cross-sections
Segmentochoron display, doe atop doe
The vertices of a dodecahedral prism of edge length 1 are given by all permutations and changes of sign of the first three coordinates of:
along with all even permutations and all sign changes of:
A dodecahedral prism has the following Coxeter diagrams:
- x x5o3o (full symmetry)
- xx5oo3oo&#x (bases considered separately)
- Bowers, Jonathan. "Category 19: Prisms" (#891).
- Klitzing, Richard. "Dope".
- Wikipedia Contributors. "Dodecahedral prism".