The Snub dodecahedron reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Snub dodecahedron

Snub dodecahedron
Click on picture for large version. Click for spinning version.
Click on picture for large version. Click for spinning version.
Type	Archimedean
Faces	80 triangles 12 pentagons
Edges	150
Vertices	60
Vertex configuration	3,3,3,3,5
Symmetry group	icosahedral (I)
Dual polyhedron	pentagonal hexecontahedron
Properties	convex, semi-regular (vertex-uniform), chiral

The snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, usually regarded as a truncated polyhedron derived by truncating either a dodecahedron or an icosahedron.

The snub dodecahedron has 92 faces, of which 12 are pentagons and the other 80 are equilateral triangles. It also has 150 edges, and 60 vertices. In three-dimensional space, it has two distinct forms, which are mirror images (or "enantiomorphs") of each other. In higher-dimensional spaces, these are congruent.

Canonical coordinates for a snub dodecahedron are all the even permutations of (±2α, ±2, ±2β), (±(α+β/τ+τ), ±(-ατ+β+1/τ), ±(α/τ+βτ-1)), (±(-α/τ+βτ+1), ±(-α+β/τ-τ), ±(ατ+β-1/τ)), (±(-α/τ+βτ-1), ±(α-β/τ-τ), ±(ατ+β+1/τ)) and (±(α+β/τ-τ), ±(ατ-β+1/τ), ±(α/τ+βτ+1)), with an even number of plus signs, where α = ξ-1/ξ, and β = ξτ+τ²+τ/ξ, where τ = (1+√5)/2 is the golden mean and ξ is the real solution to ξ³-2ξ=τ, which is the horrible number

or approximately 1.7155615.

The snub dodecahedron should not be confused with the truncated dodecahedron.

See also

• snub cube

External links

• The Uniform Polyhedra
• Virtual Reality Polyhedra The Encyclopedia of Polyhedra
• Irregular Snub Dodecahdron Wire Model Math Models, Vincent Herr

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