# Icosidodecahedral prism

(Redirected from Iddip)
Icosidodecahedral prism
Rank4
TypeUniform
SpaceSpherical
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${\displaystyle \frac{\sqrt{7+2\sqrt5}}{2} ≈ 1.69353}$
Hypervolume${\displaystyle \frac{45+17\sqrt5}{6} ≈ 13.83552}$
Dichoral anglesTrip–4–pip: ${\displaystyle \arccos\left(-\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 142.62263°}$
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).

## Vertex coordinates

The vertices of an icosidodecahedral prism of edge length 1 are given by all permutations and sign changes of the first three coordinates of:

• ${\displaystyle \left(0,\,0,\,±\frac{1+\sqrt5}{2},\,±\frac12\right),}$

along with all even permutations and all sign changes of the first three coordinates of:

• ${\displaystyle \left(±\frac12,\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac12\right).}$

## Representations

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

The regiment of the icosidodecahedral prism also includes the small icosihemidodecahedral prism and small dodecahemidodecahedral prism.