Virtual Polyhedra Created by Computer Aided Drawings on Mixing of Three Basic Forms with Cubic Symmetry

Hideo Iwasaki¹ and Teruo Noro²

¹Sobudai-Danchi 1-6-15-12, Sagamihara 228-0823, Japan
²Kasuga-cho 9-24, Hadano 259-1312, Japan

(Received June 27, 2001; Accepted July 31, 2001)

Keywords: Polyhedra, Computer Drawings, Crystal Forms, Mixing of Forms, p-q Diagrams

Abstract. The new procedure for creation of virtual polyhedra by means of computer aided drawings are presented. The essentials of procedure are based on the mixing of three basic forms such as hexahedron (cube), octahedron, and dodecahedron. The three basic forms for combinations are chosen from seven basic forms with cubic symmetry. The combinations as compounds of three forms are classified by 35-sets of "p-q diagram" on which various polyhedral forms are characterized by relative mixing rates, p and q. The 35-sets of p-q diagrams are shown in Appendix with the polyhedron and its expanded figure drawn at a set of specific values (p,q).