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Polyhedral diagrams for sections of the non-negative orthant

Published online by Cambridge University Press:  26 February 2010

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

A section of the non-negative orthant by an affine subspace is a polyhedral set. A technique, analogous to that of Gale diagrams, is described which enables one to determine the facial structure of such a polyhedral set.

Type
Research Article
Information
Mathematika , Volume 18 , Issue 2 , December 1971 , pp. 255 - 263
Copyright
Copyright © University College London 1971

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References

1Grünbaum, B., Convex Polytopes (London-New York-Sydney, 1967).Google Scholar
2Grünbaum, B.,* “Polytopes, graphs and complexes ”, Bull. American Math. Soc., (1970), 1131–1201.CrossRefGoogle Scholar
3Grünbaum, B., and Shephard, G. C.,* “Convex polytopes ”, Bull. London Math. Soc., 1 (1969), 257–300.CrossRefGoogle Scholar
4McMullen, P., On Convex Polytopes, Ph.D. Thesis, University of Birmingham, 1968.Google Scholar
5McMullen, P., “On zonotopes ”, Trans. Amer. Math. Soc., 159 (1971), 91–109.CrossRefGoogle Scholar
6McMullen, P., and Shephard, G. C., “Diagrams for centrally symmetric polytopes ”, Mathematika, 15 (1968), 123–138.CrossRefGoogle Scholar
7McMullen, P. and Shephard, G. C., “Polytopes with an axis of symmetry ”, Canadian J. of Math., 22 (1970), 265–287.CrossRefGoogle Scholar
8McMullen, P. and Shephard, G. C., Convex Polytopes and the Upper Bound Conjecture, London Math. Soc. Lecture Notes No. 3, (Cambridge, 1971).CrossRefGoogle Scholar
9McMullen, P. and Shephard, G. C., “Representations and diagrams ” (in preparation).Google Scholar
10Shephard, G. C., Neighbourliness and Radon's Theorem ”, Mathematika, 16 (1969), 273–275.CrossRefGoogle Scholar
11Shephard, G. C., “Diagrams for positive bases ”, J. London Math. Soc. (2), 4 (1971), 165–175.CrossRefGoogle Scholar