# Truncated dodecahedral prism

Truncated dodecahedral prism Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymTiddip
Coxeter diagramx x5x3o (       )
Elements
Cells20 triangular prisms, 12 decagonal prisms, 2 truncated dodecahedra
Faces40 triangles, 30+60 squares, 24 decagons
Edges60+60+120
Vertices120
Vertex figureSphenoid, edge lengths 1, 10+25/2, 10+25/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius$\sqrt{\frac{39+15\sqrt5}{8}} ≈ 3.01125$ Hypervolume$5\frac{99+47\sqrt5}{12} ≈ 85.03966$ Dichoral anglesTrip–4–dip: $\arccos\left(-\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 142.62263°$ Dip–4–dip: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$ Tid–10–dip: 90°
Tid–3–trip: 90°
Height1
Central density1
Number of pieces34
Level of complexity12
Related polytopes
ArmyTiddip
RegimentTiddip
DualTriakis icosahedral tegum
ConjugateQuasitruncated great stellated dodecahedral prism
Abstract properties
Flag count2880
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexYes
NatureTame

The truncated dodecahedral prism or tiddip is a prismatic uniform polychoron that consists of 2 truncated dodecahedra, 12 decagonal prisms, and 20 triangular prisms. Each vertex joins 1 truncated dodecahedron, 1 triangular prism, and 2 decagonal prisms. It is a prism based on the truncated dodecahedron. As such it is also a convex segmentochoron (designated K-4.130 on Richard Klitzing's list).

## Vertex coordinates

The vertices of a truncated dodecahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:

• $\left(0,\,±\frac12,\,±\frac{5+3\sqrt5}{4},\,±\frac12\right),$ • $\left(±\frac12,\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{2},\,±\frac12\right),$ • $\left(±\frac{3+\sqrt5}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{2+\sqrt5}{2},\,±\frac12\right).$ ## Representations

A truncated dodecahedral prism has the following Coxeter diagrams:

• x x5x3o (full symmetry)
• xx5xx3oo&#x (bases considered separately)