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Facetting diagrams

Published online by Cambridge University Press:  01 August 2016

Guy Inchbald
Guy Inchbald*
Affiliation:
Park View, Queenhill, Upton-upon-Severn, Worcester WR8 0RE
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Extract

Facetting, or faceting, is the process of removing parts of a polyhedron, without creating any new vertices. It has received far less attention than the process of stellation, which is its exact reciprocal. Facetting is perhaps less easy to visualise clearly, and the results may not have the same immediate appeal. But once broached, it has a fascination all its own. Also, to understand the rules of stellation properly, it can be illuminating to study the reciprocal rules of facetting. Now that suitable software is available (see Further investigations), the study of facetting is gaining momentum.

Type
Articles
Information
The Mathematical Gazette , Volume 90 , Issue 518 , July 2006 , pp. 253 - 261
Copyright
Copyright © The Mathematical Association 2006

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References

1. Bridge, N. J. Facetting the dodecahedron, Acta Crystallographica A30 (1974), pp. 548–552.CrossRefGoogle Scholar
2. Inchbald, G. Towards stellating the icosahedron and faceting the dodecahedron, Symmetry: Culture and Science Vol. 11, 1–4 (2000) pp. 269–291. Also available at: http://www.steelpillow.com/polyhedra/icosa/stelfacet/StelFacet.htm.Google Scholar
3. Inchbald, G. Tidy dodecahedra and icosahedra. Includes extensive comments on Bridge’s paper. Available at: http://www.steelpillow.com/polyhedra/icosa/tidystelfacet/TidyStelFacet.htm.Google Scholar
4. Stella, Great available from: http://www.software3d.com/Stella.html.Google Scholar
5. Wenninger, M. Dual Models, Cambridge (1983 hbk, 2003 pbk).CrossRefGoogle Scholar