Dodecahedral prism
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 K4.74 on Richard Klitzing's list).
Dodecahedral prism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Dope 
Coxeter diagram  x x5o3o () 
Elements  
Cells  12 pentagonal prisms, 2 dodecahedra 
Faces  30 squares, 24 pentagons 
Edges  20+60 
Vertices  40 
Vertex figure  Triangular pyramid, edge lengths (1+√5)/2 (base), √2 (legs) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Pip–4–pip: 
Doe–5–pip: 90°  
Height  1 
Central density  1 
Number of external pieces  14 
Level of complexity  4 
Related polytopes  
Army  Dope 
Regiment  Dope 
Dual  Icosahedral tegum 
Conjugate  Great stellated dodecahedral prism 
Abstract & topological properties  
Flag count  960 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  H_{3}×A_{1}, order 240 
Convex  Yes 
Nature  Tame 
Gallery edit

Segmentochoron display, doe atop doe

Net
Vertex coordinates edit
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:
 .
Representations edit
A dodecahedral prism has the following Coxeter diagrams:
 x x5o3o ( ) (full symmetry)
 xx5oo3oo&#x (bases considered separately)
External links edit
 Bowers, Jonathan. "Category 19: Prisms" (#891).
 Klitzing, Richard. "Dope".
 Wikipedia contributors. "Dodecahedral prism".