Icosidodecahedral prism
Icosidodecahedral prism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Iddip 
Coxeter diagram  x o5x3o () 
Elements  
Cells  20 triangular prisms, 12 pentagonal prisms, 2 icosidodecahedra 
Faces  40 triangles, 60 squares, 24 pentagons 
Edges  30+120 
Vertices  60 
Vertex figure  Rectangular pyramid, edge lengths 1, (1+√5)/2 (base), √2 (legs) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Trip–4–pip: 
Id–3–trip: 90°  
Id–5–pip: 90°  
Height  1 
Central density  1 
Number of external pieces  34 
Level of complexity  8 
Related polytopes  
Army  Iddip 
Regiment  Iddip 
Dual  Rhombic triacontahedral tegum 
Conjugate  Great icosidodecahedral prism 
Abstract & topological properties  
Flag count  1920 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  H_{3}×A_{1}, order 240 
Convex  Yes 
Nature  Tame 
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 K4.90 on Richard Klitzing's list).
Gallery[edit  edit source]

Segmentochoron display, id atop id

Net
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 (H_{2}×A_{1} axial, pentagonal prismfirst)
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".