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The maximum numbers of faces of a convex polytope
Author(s) -
McMullen P.
Publication year - 1970
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300002850
Subject(s) - mathematics , combinatorics , polytope , convex polytope , conjecture , regular polygon , birkhoff polytope , upper and lower bounds , uniform k 21 polytope , convex analysis , convex set , geometry , convex optimization , mathematical analysis
In this paper we give a proof of the long‐standing Upper‐bound Conjecture for convex polytopes, which states that, for 1 ≤ j < d < v , the maximum possible number of j ‐faces of a d ‐polytope with v vertices is achieved by a cyclic polytope C ( v, d ).