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Shaping Space pp 223-229 | Cite as

Polyhedra Analogues of the Platonic Solids

  • Jörg M. Wills
Chapter

Abstract

In this chapter we investigate polyhedra in Euclidean 3-space, E 3, without self-intersections and with some local and global properties related to those of the Platonic solids. A polyhedron is the geometric realization of a compact 2-manifold in E 3 such that its 2-faces are (not necessarily convex) plane polygons bounded by finitely many line segments. Adjacent faces and edges are not coplanar. A flag of a polyhedron P is any triple consisting of a vertex, an edge, and a face of P, all mutually incident.

Keywords

Automorphism Group Geometric Realization Regular Hexagon Regular Polyhedron Platonic Solid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.SiegenGermany

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