Main Page | See live article | Alphabetical index 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. 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 plusses, 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 3√((τ+√(τ-5/27))/2)+3√((τ-√(τ-5/27))/2). 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. The snub dodecahedron should not be confused with the truncated dodecahedron. External Links The Uniform Polyhedra Virtual Reality Polyhedra The Encyclopedia of Polyhedra This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.