Icosidodecahedral prism

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Icosidodecahedral prism
Icosidodecahedral prism.png
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymIddip
Coxeter diagramx o5x3o (CDel node 1.pngCDel 2.pngCDel node.pngCDel 5.pngCDel node 1.pngCDel 3.pngCDel node.png)
Elements
Cells20 triangular prisms, 12 pentagonal prisms, 2 icosidodecahedra
Faces40 triangles, 60 squares, 24 pentagons
Edges30+120
Vertices60
Vertex figureRectangular pyramid, edge lengths 1, (1+5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTrip–4–pip:
 Id–3–trip: 90°
 Id–5–pip: 90°
Height1
Central density1
Number of external pieces34
Level of complexity8
Related polytopes
ArmyIddip
RegimentIddip
DualRhombic triacontahedral tegum
ConjugateGreat icosidodecahedral prism
Abstract & topological properties
Flag count1920
Euler characteristic0
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexYes
NatureTame

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]

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]