truncated icosahedron

plural truncated icosahedra · plural truncated icosahedrons

1. geometryA 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.

   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?

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   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.

   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.

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

   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).

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

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

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