Main Page | See live article | Alphabetical index The truncated icosahedron is an Archimedean solid. It has the same shape as a football or a 60-carbon fullerene. Canonical coordinates for the vertices of a truncated icosahedron centered at the origin are the orthogonal rectangles (0,±1,±3τ), (±1,±3τ,0), (±3τ,0,±1) and the orthogonal bricks/3D-rectangles (±2,±(1+2τ),±τ), (±(1+2τ),±τ,±2), (±τ,±2,±(1+2τ)) along with the ortogonal bricks/3D-rectangles (±1,±(2+τ),±2τ), (±(2+τ),±2τ,±1), (±2τ,±1,±(2+τ)), where τ = (1+√5)/2 is the golden mean. It has 12 regular pentagonal faces, 20 regular hexagonal faces, 60 vertices and 90 edges. One easily verifies Euler's formula for polyhedra (see Leonhard Euler): 32 + 60 = 90 + 2. A football is like this polyhedron except that it is more spherical, because the faces bulge due the pressure of the air inside. It is also a model for the Buckminsterfullerene (C60) molecule. The diameter of the football and this buckyball are 22 cm and ca. 1 nm, respectively, hence the size ratio is 200,000,000 : 1. See also: Icosahedron and 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.