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A dual for Descartes’ theorem on polyhedra

Published online by Cambridge University Press:  01 August 2016

Branko Grünbaum  and
G. C. Shephard
Branko Grünbaum
Affiliation:
University of Washington, Seattle, WA 98195, USA
G. C. Shephard
Affiliation:
University of East Anglia, Norwich NR4 7TJ
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Extract

The theory of duality is well known as a useful tool in the study of convex three-dimensional polyhedra. For example, if we know the types of polyhedra that can be circumscribed about a sphere, duality provides an immediate answer to the question as to what types can be inscribed in a sphere. Theorems like Euler’s Theorem (V – E + F = 2 where V, E and F are the numbers of vertices, edges and faces of a convex polyhedron) are self-dual in the sense that duality simply interchanges the values of V and F.

Type
Research Article
Information
The Mathematical Gazette , Volume 71 , Issue 457 , October 1987 , pp. 214 - 216
Copyright
Copyright © The Mathematical Association 1987

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References

1. Federico, P.J., Descartes on Polyhedra. Springer-Verlag, New York, Heidelberg, Berlin 1982.Google Scholar
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3. Hilton, P. and Pedersen, J. Discovering modifyhing and solving problems: a case study from the contemplation of polyhedra. (To appear in Teaching and learning: a focus on problem solving, soon to be published by the National Council of Teachers of Mathematics.)Google Scholar