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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Indecomposable polytopes


Author: Walter Meyer
Journal: Trans. Amer. Math. Soc. 190 (1974), 77-86
MSC: Primary 52A25
DOI: https://doi.org/10.1090/S0002-9947-1974-0338929-4
MathSciNet review: 0338929
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Abstract: The space of summands (with respect to vector addition) of a convex polytope in n dimensions is studied. This space is shown to be isomorphic to a convex pointed cone in Euclidean space. The extreme rays of this cone correspond to similarity classes of indecomposable polytopes. The decomposition of a polytope is described and a bound is given for the number of indecomposable summands needed. A means of determining indecomposability from the equations of the bounding hyperplanes is given.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0338929-4
Keywords: Convex cone, decomposition, extreme ray, indecomposable, polytope, vector addition, Minkowski addition
Article copyright: © Copyright 1974 American Mathematical Society