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A note on polyhedral cones

Published online by Cambridge University Press:  09 April 2009

Bit-Shun Tam
Bit-Shun Tam
Affiliation:
Department of Mathematics, University of Hong Kong, Hong Kong.
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Abstract

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In this short note, two results on a solid, pointed, closed cone C in Rn will be given: first, C is polyhedral iff it has a finite number of maximal faces; second, for any face F of C, C* ∩ F┴ is a face of its dual cone C* of dimension n – dim F.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 4 , December 1976 , pp. 456 - 461
Copyright
Copyright © Australian Mathematical Society 1976

References

Barker, G. P. (1973), ‘The lattice of faces of a finite dimensional cone’, Linear Algebra and Appl. 7, 71–82.CrossRefGoogle Scholar
McMullen, P. and Shephard, G. C. (1971), Convex Polytopes and the Upper Bound Conjecture (C. U. P., London, 1971).CrossRefGoogle Scholar
Stoer, J. and Witzgall, C. (1970), Convexity and Optimization in Finite Dimensions I (Springer, Berlin - Heidelberg - New York, 1970).CrossRefGoogle Scholar