pentakis dodecahedron

English

Alternative forms

  • pentakisdodecahedron

Noun

pentakis dodecahedron (plural pentakis dodecahedra)

  1. (mathematics) A 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.
    • 1990, Peter Pearce, Structure in Nature Is a Strategy for Design‎[1], page 161:
      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.

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