Titlebook: Convex Polytopes; Branko Grünbaum,Volker Kaibel,Victor Klee,Günter M Textbook 2003Latest edition Springer Science+Business Media New York

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https://doi.org/10.1007/978-0-387-49431-9In the preceding chapter s we became acquainted with methods of generating convex polytopes and with the relations existing among a polytope and its faces or other points of the space. Our interest was mostly centered on positional relationships between a polytope (or its faces) and some other given geometric object.

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Two-Layer Quasi-Geostrophic Models,In chapter 8 we have seen that the affine hull of the .(..) of .-vectors of all .-polytopes is the Euler hyperplane. In the present chapter we shall be interested in finding the affine hulls of sets .(.), for certain families . of .-polytopes.

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Two-Layer Quasi-Geostrophic Models,In chapter 11 we have investigated some properties of complexes realizable by skeletons of polytopes. The present chapter complements this by discussing the known results on the uniqueness of such realizations.

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Two-Layer Quasi-Geostrophic Models,There are many fields which are similar in spirit and related in the methods used and results obtained to the combinatorial theory of polytopes. The present chapter is devoted to one such field: to questions dealing with arrangements of (or partitions by) hyperplanes.

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Polytopes,The present chapter contains the fundamental concepts and facts on which we rely in the sequel. Polytopes, their faces and combinatorial types, complexes, Schlegel diagrams, combinatorial equivalence, duality, and polarity are the main topics discussed.

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Examples,The aim of the present chapter is to describe in some detail certain polytopes and families of polytopes. This should serve the double purpose of familiarizing the reader with geometric relationships in higher-dimensional spaces, as well as providing factual material which will be used later on.