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An Elementary Proof of Gram's Theorem for Convex Polytopes

Published online by Cambridge University Press:  20 November 2018

G. C. Shephard
G. C. Shephard*
Affiliation:
University of East Anglia, England
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Let P be a d-polytope (that is, a d-dimensional convex polytope in Euclidean space) and for 0 ≤ j ≤ d – 1 let (i = 1, . . . ,ƒj(P)) represent its j-faces. Associated with each face is a non-negative number ϕ(P, ), to be defined later, which is called the interior angle of P at the face .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1214 - 1217
Copyright
Copyright © Canadian Mathematical Society 1967

References

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5. Sommerville, D. M. Y., The relations connecting the angle-sums and volume of a polytope in space of n dimensions, Proc. Roy. Soc. London, Ser. A, 115 (1927), 103–119.Google Scholar