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

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Neighborly Polytopes,The neighborly polytopes, rediscovered barely a decade ago as a rather freakish family of polytopes, have in recent years gained importance and received much attention due to their connection with certain extremal problems (see section 10.1). In the present chapter we discuss the main properties of neighborly polytopes.

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,Euler’s Relation,In 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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Properties of Boundary Complexes,In the present chapter we shall study in more detail the facial structure of polytopes by investigating some properties of the boundary complexes of polytopes, and some of their subcomplexes.

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Angle-sums Relations; the Steiner Point,The subject matter of the present chapter differs from the foregoing parts of the book in being dependent on the structure of .. as a Euclidean space. In spirit, however, the topic is closely related to the material of chapters 8 and 9.

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Diameters of Polytopes,This and the next chapter are concerned with paths on polytopes. References are given, unsolved problems are stated, and some outlines of proofs are included. Most of the results have previously appeared in the literature but a few of them are new.

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