Icosidodecahedral prism

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Icosidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymIddip
Coxeter diagramx o5x3o ()
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]