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Convex polygons as carriers
Published online by Cambridge University Press: 14 March 2016
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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.
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