pentakis dodecahedron

plural pentakis dodecahedra · alternative pentakisdodecahedron

1. mathematicsA Catalan solid equivalent to a dodecahedron with a pentagonal pyramid covering each face, in the end having 60 isosceles triangle faces, 90 edges, and 32 vertices.

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   The pentakis dodecahedron with its full icosahedral symmetry illustrates the fact that it is impossible to form a convex polyhedron with more than sixty identical non-right triangles. If right triangles are permitted then each isosceles triangle of the pentakis dodecahedron can be sub-divided into two coplanar right triangles, giving 120 as the greatest number of like units which can be used to form a convex polyhedron. It is this 120th lowest-common-denominator "icosahedral triangle" from which Fuller has derived his geodesic domes. The pentakis dodecahedron is topologically equivalent to the simplest of Fuller's geodesic domes.

   1990, Peter Pearce, Structure in Nature Is a Strategy for Design, page 161