truncated icosahedron

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truncated icosahedron

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Truncated icosahedron

From truncated + icosahedron.

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  regular truncated icosahedron
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  C₆₀: buckminsterfullerene
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  A soccer ball with a regular truncated icosahedron

truncated icosahedron (plural truncated icosahedra or truncated icosahedrons)

1. (geometry) A polyhedron that has thirty-two faces (12 regular pentagons and 20 regular hexagons) and 60 vertices and 90 edges, and is one of the Archimedean solids.

   A truncated icosahedron may be formed by truncating the vertices of an icosahedron. Each vertex of the icosahedron is replaced by a pentagonal face and each triangular face of the icosahedron is replaced by a hexagonal face, which is inscribed inside the triangular face of the original icosahedron. The entire resulting truncated icosahedron is thus fittingly inscribed inside the original icosahedron.

   • 1989, Tony Rothman, Science a la Mode: Physical Fashions and Fictions‎, page 64:

     This is the truncated icosahedron. Where the five triangles meet to form a vertex is now a pentagon, and a hexagon now replaces each triangular face. Therefore, the truncated icosahedron is composed of twelve pentagons and twenty hexagons.

   • 1993, R. Bruce King, Applications of Graph Theory and Topology in Inorganic Cluster and Coordination Chemistry‎, page 183:

     In addition to the 20 lithium atoms in layer b, additional lithium atoms (layer e) are located above the twelve pentagonal faces of the peripheral truncated icosahedra which, because of the way that the truncated icosahedra are linked, simultaneously cap the pentagonal faces of two adjacent truncated icosahedra sharing an edge (sharing method 1 above).

   • 2001, Edward A. Rietman, Molecular Engineering of Nanosystems‎, page 130:

     Fullerenes are truncated icosahedrons with 90 edges of equal length, 60 vertices, 20 hexagonal faces, and 12 pentagonal faces that form a closed shell.

   • 2008, Jill Vincent, Andy Edwards, David Tynan, Gloria Stillman (editors), MathsWorld Year Eight for Queensland, Teacher Edition, page 308,

     Do you know which sport is played with a truncated icosahedron?