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Vol. 40 (1999) No. 2 April n. 130


The chiral polyhedra

< Table of Contents for Vol. 40 (1999) No. 2 April n. 130
  • Journal Name: Journal of the International Association for Shell and Spatial Structures (J. IASS)
  • ISSN: (Electronic Version) 1996-9015
  • ISSN: (Print Version) 1028-365X
  • Issue: Vol. 40 (1999) No. 2 April n. 130
  • Title: The chiral polyhedra
  • Author(s): P. Huybers
  • Keywords: structural morphology, snub solids
Abstract
'Chirality' of a certain form means that it is not super-imposable on its mirror image. Most of the regular and semi-regular polyhedra have identical original and mirror images but there are two that have a mirror image that is different. This means that they have a left-handed and a right-handed version. These two polyhedra are the so-called ‘snub solids', the snub cube and the snub dodecahedron, that consist of a number of triangles and a number of either squares or pentagons respectively. They have interesting characteristics, that - on closer examination - appear to be applicable to a few other forms as well. The semi-regular polyhedra are generally considered as to be found by truncation of the regular solids, either according their vertices or according their edges or both. In the snub solids this truncation is done twice per edge and under a certain angle with respect to this edge and to each other, so that two triangular faces per original edge occur. The snub solids both have a left-handed and a right-handed version, that are 'enantiomorphic' (see Fig. 1). They are much more complicated than the other polyhedra. It is therefore interesting to consider their geometry in more detail, particularly as some representatives are often used as a basis for a further subdivision of spherical surfaces. The present paper is a further elaboration of a contribution by the same author to the IASS conference of 1992 in Toronto (Ref. 7).

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