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.
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© 2013 Springer Science+Business Media New York
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Wills, J.M. (2013). Polyhedra Analogues of the Platonic Solids. In: Senechal, M. (eds) Shaping Space. Springer, New York, NY. https://doi.org/10.1007/978-0-387-92714-5_17
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DOI: https://doi.org/10.1007/978-0-387-92714-5_17
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Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-92713-8
Online ISBN: 978-0-387-92714-5
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