CONVEX EQUILATERAL POLYHEDRA WITH POLYHEDRAL SYMMETRY

摘要

A new class of polyhedron is constructed by decorating each of the triangular facets of an icosahedron with the T vertices and connecting edges of a “Goldberg triangle.” A unique set of internal angles in each planar face of each new polyhedron is then obtained, for example by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, where the independent variables are a subset of the internal angles in 6 gons. Alternatively, an iterative method that solves for angles within each hexagonal ring may be solved for that nulls dihedral angle discrepancy throughout the polyhedron. The 6 gon faces in the resulting “Goldberg polyhedra” are equilateral and planar, but not equiangular, and nearly spherical.