Handbook of Structure Part I: Polyhedra and Spheres

摘要

The work comprises the first part of a series of descriptive handbooks on geometry and structure. It contains basic information on the following: (1) the five Platonic polyhedra, 13 Archimedian semi-regular polyhedra, and 13 Archimedian dual polyhedra; (2) a method for comparing surface areas and volumes of polyhedra; (3) a description of one system of basic subdivisions of the tetrahedron and the octahedron into smaller components; (4) infinite packings of circles in two dimensions and infinite packings of spheres in three dimensions; (5) polyhedra that may be defined by sphere packings; (6) methods of packing polyhedra in various combinations to fill space; (7) a method of accounting for volumes of polyhedra based on a tetrahedron with a normalized edge and a volume set at unity; and (8) methods of physically deriving polyhedra by various operations: folding the two dimensional net, creating the dual of a polyhedron, truncating the vertices and edges of a polyhedron, rotating and translating polygon faces from one position to another, and fusing and separating vertices of polyhedra.