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## Icosahedronicosahedron [ˌaıkəsə'hiːdrən] noun (plural: -drons, -dra [-drə])
a solid figure having 20 faces. The faces of a regular icosahedron are equilateral triangles.
[Etymology: 16th Century: from Greek eikosaedron, from eikosi twenty + -edron -hedron], "icosa'hedral adjective
In geometry, the
Canonical coordinates for the vertices of an icosahedron centered at the origin are (0,±1,±τ), (±1,±τ,0), (±τ,0,±1), where τ = (1+√5)/2 is the golden mean - note these form three mutually orthogonal golden rectangles. The 20 edges of an octahedron can be partitioned in the golden mean so that the resulting vertices define a regular icosahedron; the five octahedra defining any given icosahedron form a regular polyhedral compound.
Many viruses, including HIV, have the shape of an icosahedron. Viruses need to be small, and the icosahedron is the regular polyhedron with largest volume per diameter. A
There are distortions of the icosahedron that, while no longer regular, are nevertheless vertex-uniform. These are invariant under the same rotations as the tetrahedron, and are somewhat analogous to the snub cube and snub dodecahedron, including some forms which are chiral and some with T See also Truncated icosahedron. ## External Links- The Uniform Polyhedra
- Virtual Reality Polyhedra The Encyclopedia of Polyhedra
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