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Convex polytopes with convex nets

Published online by Cambridge University Press:  24 October 2008

G. C. Shephard
G. C. Shephard
Affiliation:
University of East Anglia, Norwich NR4 7TJ, England
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Extract

The idea of a net will be familiar to anyone who has made a model of a three-dimensional convex polytope (3-polytope) out of a flat sheet of card or similar material. To begin with, one cuts out a polygon, and then the model is formed by folding this and joining its edges in an appropriate manner. For example, Fig. 1 illustrates two nets for a regular tetrahedron. The folds are indicated by broken lines and lettering (either of the edges or of the vertices) indicates how the edges are to be joined.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 3 , November 1975 , pp. 389 - 403
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Alexandrow, A. D.Konvexe Polyeder. [German translation] (Berlin, 1958.)Google Scholar
(2)Barnette, D. W.Dense sets of polytopes in P 3. Aeq. Math. 7 (1972), 28–35.CrossRefGoogle Scholar
(3)Cundy, H. M. and Rollett, A. P.Mathematical Models. (Oxford, 1952.)Google Scholar
(4)Grünbaum, B.Convex Polytopes. (London–New York–Sydney, 1967.)Google Scholar
(5)Hodge, W. V. D. and Pedoe, D.Methods of Algebraic Geometry, Vol. 1. (Cambridge–New York, 1947.)Google Scholar
(6)McMullen, P. and Shephard, G. C.Convex Polytopes and the Upper Bound Conjecture. (Cambridge–New York, 1971.)Google Scholar
(7)Moon, J. W. and Moser, L.Simple paths on polyhedra. Pacific J. Math. 13 (1963), 629–631.Google Scholar
(8)Shephard, G. C.Subpolytopes of stack polytopes. Israel J. Math. 19 (1974), 292–296.CrossRefGoogle Scholar
(9)Steinitz, E. and Rademacher, H.Vorlesungen über die Theorie der Polyeder. (Berlin, 1934.)Google Scholar