HANDBOOK OF STRUCTURE PART I: POLYHEDRA AND SPHERES.
Research Communication no. 75,
DOUGLAS AIRCRAFT CO INC HUNTINGTON BEACH CALIF ADVANCED RESEARCH LABS
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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.
- Theoretical Mathematics