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On Rational Subdivisions of Polyhedra with Rational Vertices

Published online by Cambridge University Press:  20 November 2018

W. M. Beynon
W. M. Beynon*
Affiliation:
University of Warwick, Coventry, England
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Abstract

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This short paper is devoted to the proof of a single theorem, which, in its simplest form, asserts that if Q is a polyhedron in Rn which can be expressed as the union of finitely many convex polytopes whose vertices are at rational points in Rn, and if is a simplicial subdivision of Q﹜ then there is an isomorphic simplicial subdivision ” of Q in which all vertices are at rational points.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 238 - 242
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Beynon, W. M., Applications of duality in the theory of finitely generated lattice-ordered Abelian groups (to appear).Google Scholar
2. Glaser, L. C., Geometrical combinatorial topology, Vol. 1, Van Nostrand Reinhold Mathematical Studies 27.Google Scholar
3. Stallings, J. R., Lectures on polyhedral topology, Tata Institute of Fundamental Research, Bombay (1968).Google Scholar