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Convex polygons as carriers

Published online by Cambridge University Press:  14 March 2016

G. C. Shephard
G. C. Shephard*
Affiliation:
School of Mathematics, University of East Anglia, Norwich, NR4 7TJ e-mail: [email protected]
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Extract

We shall use the word ‘polyhedron’ to mean a connected, simply-connected 3-polytope of positive (non-zero) volume. The idea of the net of a polyhedron P is well known. For example, the regular octahedron has eleven distinct nets, three of which are shown in Figure 1. A net consists of three parts:

  • (a) A plane connected and simply-connected polygon Q (denoted by heavy lines in the diagrams), known as the carrier of the net;

    (b) A set of lines known as, fold-lines in the interior of Q;

    (c) A labelling of the edges of Q.

    If one cuts Q out of paper or similar material, folds it along the fold-lines, and then pastes together edges with matching labels, one obtains a model of the polyhedron P. We say that a net is convex if, and only if, its carrier Q is convex.

Type
Research Article
Information
The Mathematical Gazette , Volume 100 , Issue 547 , March 2016 , pp. 93 - 102
Copyright
Copyright © Mathematical Association 2016 

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References

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