Small rhombicosidodecahedral prism
Small rhombicosidodecahedral prism  

Rank  4 
Type  Uniform 
Notation  
Bowers style acronym  Sriddip 
Coxeter diagram  x x5o3x () 
Elements  
Cells  20 triangular prisms, 30 cubes, 12 pentagonal prisms, 2 small rhombicosidodecahedra 
Faces  40 triangles, 60+60+60 squares, 24 pentagons 
Edges  60+120+120 
Vertices  120 
Vertex figure  Isosceles trapezoidal pyramid, edge lengths 1, √2, (1+√5)/2, √2 (base), √2 (legs) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dichoral angles  Trip–4–cube: 
Cube–4–pip:  
Srid–5–pip: 90°  
Srid–3–trip: 90°  
Srid–4–cube: 90°  
Height  1 
Central density  1 
Number of external pieces  64 
Level of complexity  16 
Related polytopes  
Army  Sriddip 
Regiment  Sriddip 
Dual  Deltoidal hexecontahedral tegum 
Conjugate  Quasirhombicosidodecahedral prism 
Abstract & topological properties  
Flag count  3840 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  H_{3}×A_{1}, order 240 
Convex  Yes 
Nature  Tame 
The small rhombicosidodecahedral prism or sriddip is a prismatic uniform polychoron that consists of 2 small rhombicosidodecahedra, 12 pentagonal prisms, 20 triangular prisms, and 30 cubes. Each vertex joins 1 small rhombicosidodecahedron, 1 pentagonal prism, 1 triangular prism, and 2 cubes. As the name suggests, it is a prism based on the small rhombicosidodecahedron. As such it is also a convex segmentochoron (designated K4.111 on Richard Klitzing's list).
The small rhombicosidodecahedral prism can be vertexinscribed into the small ditetrahedronary hexacosihecatonicosachoron.
Gallery[edit  edit source]

Card with cell counts, verf, and crosssections

Segmentochoron display, srid atop srid

Net
Vertex coordinates[edit  edit source]
The vertices of a small rhombicosidodecahedral prism of edge length 1 are given by all permutations of the first three coordinates of:
along with all even permutations of the first three coordinates of:
Representations[edit  edit source]
The small rhombicosidodecahedral prism has the following Coxeter diagrams:
 x x5o3x (full symmetry)
 xx5oo3xx&#x (bases considered separately)
Related polychora[edit  edit source]
The pentagonal cupolic prism is a segmentochoron that can be obtained as a cap of the small rhombicosidodecahedral prism.
The regiment of the small rhombicosidodecahedral prism also includes the small dodecicosidodecahedral prism and the small rhombidodecahedral prism.
External links[edit  edit source]
 Bowers, Jonathan. "Category 19: Prisms" (#926).
 Klitzing, Richard. "Sriddip".
 Wikipedia contributors. "Rhombicosidodecahedral prism".