Truncated dodecahedron

Truncated dodecahedron
(Click here for rotating model)
Type	Archimedean solid
Elements	F=32, E=90, V=60 (χ=2)
Faces by sides	20{3}+12{10}
Schläfli symbol	t{5,3}
Wythoff symbol	2 3 \| 5
Symmetry group	I_h
Index references	U₂₆, C₂₉, W₁₀
Dual	Triakis icosahedron
Properties	Semiregular convex
Vertex figure 3.10.10

A colored model

In geometry, the truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges.

[edit] Geometric relations

This polyhedron can be formed from a dodecahedron by truncating (cutting off) the corners so the pentagon faces become decagons and the corners become triangles.

The following Cartesian coordinates define the vertices of a truncated dodecahedron centered at the origin:

(0, ±1/τ, ±(2+τ))

(±(2+τ), 0, ±1/τ)

(±1/τ, ±(2+τ), 0)

(±1/τ, ±τ, ±2τ)

(±2τ, ±1/τ, ±τ)

(±τ, ±2τ, ±1/τ)

(±τ, ±2, ±τ²)

(±τ², ±τ, ±2)

(±2, ±τ², ±τ)

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).

Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)