Goldberg's Method Extends Through To Platonic Polyhedra

Goldberg got a class of polyhedra which are icosahedral symmetry by appending hexagons on regular dodecahedron by rule in 1937. They are called Goldberg polyhedra which provides a new approach for polyhedral molecule design.This paper extends his method to other platonic polyhedra. We obtain three classes of polyhedra which have high symmetry. they are regular tetrahedral class belonging to tetrahedral group , regular hexahedral class and regular octahedral class belonging to octahedral group. Besides we analyze and character their geometrical properties and the rule of growth. It can provide theoretical countenance for DNA polyhedral synthesis and protein polyhedral links construction.