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A conjecture for polytopes

Published online by Cambridge University Press:  24 October 2008

J. N. Lillington
J. N. Lillington
Affiliation:
Royal Holloway College, Englefield Green, Surrey
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Extract

All sets considered in this paper will be subsets of n-dimensional Eucidean space En. In this paper, we shall consider the ‘total edge-lengths’ of polytopes which are inscribed in a given sphere and which contain its centre. We first, however, mention some related problems considered by various authors which may be of interest to the reader.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 2 , September 1974 , pp. 407 - 411
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Fejes, Toth L.On the total length of the edges of a polyhedron. Norske. Vid. Selsk. Forh. (Trondheim) 21 (1948), 32–4.Google Scholar
(2)Fejes, Toth L.Lagerungen in der Efene auf der Kugel und im Roum (Berlin, 1953).Google Scholar
(3)Hammersley, J. M.The total length of the edges of a polyhedron. Compositio Math. 9 (1951), 239–40.Google Scholar
(4)Besicovitch, A. S. and Eggleston, H. G.The total length of the edges of a polyhedron. Quart. J. Math. Oxford 8 (1957), 172–190.CrossRefGoogle Scholar
(5)Besicovitch, A. S.A net to hold a sphere. Math. Gaz. 41 (1957), 106–107.CrossRefGoogle Scholar
(6)Besicovitch, A. S.A cage to hold a unit-sphere. Proc. Symposia in Pure Math. 7 (1963), 19–20.CrossRefGoogle Scholar
(7)Aberth, O.An isoperimetric inequality for polyhedra and its application to an extremal problem. Proc. London Math. Soc. 13 (1963), 322–336.CrossRefGoogle Scholar
(8)Melzax, Z. A.Problems connected with convexity. Canad. Math. Bull. 9 (1965), 565–573.CrossRefGoogle Scholar
(9)Aberth, A.An inequality for convex polyhedra. J. London Math. Soc. (2) 6 (1973), 382–384.CrossRefGoogle Scholar
(10)Grunbaum, B.Convex polytopes. (John Wiley and Sons; London, New York, Sydney, 1967).Google Scholar
(11)Eggleston, H. G., Grunbaum, B. and Klee, V.Some semicontinuity theorems for convex polytopes and cell-complexes. Comment. Math. Helv. 39 (1964), 165–188.CrossRefGoogle Scholar