Truncated dodecahedral prism

Truncated dodecahedral prism
	(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Tiddip
Coxeter diagram	x x5x3o ()
Elements
Cells	20 triangular prisms, 12 decagonal prisms, 2 truncated dodecahedra
Faces	40 triangles, 30+60 squares, 24 decagons
Edges	60+60+120
Vertices	120
Vertex figure	Sphenoid, edge lengths 1, √10+2√5/2, √10+2√5/2 (base), √2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral angles	Trip–4–dip:
	Dip–4–dip:
	Tid–10–dip: 90°
	Tid–3–trip: 90°
Height	1
Central density	1
Number of pieces	34
Level of complexity	12
Related polytopes
Army	Tiddip
Regiment	Tiddip
Dual	Triakis icosahedral tegum
Conjugate	Quasitruncated great stellated dodecahedral prism
Abstract properties
Flag count	2880
Euler characteristic	0
Topological properties
Orientable	Yes
Properties
Symmetry	H3×A1, order 240
Convex	Yes
Nature	Tame

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).

Gallery[edit | edit source]

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

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

A truncated dodecahedral prism has the following Coxeter diagrams: