Neighborliness of the Symmetric Moment Curve
نویسندگان
چکیده
in R, where t ranges over the unit circle S = R/2πZ. The curve Uk(t) is locally neighborly: as long as t1, . . . , tk lie in an open arc of S of a certain length φk > 0, the convex hull of the points Uk (t1) , . . . , Uk (tk) is a face of Bk. We characterize the maximum possible length φk, proving, in particular, that φk > π/2 for all k and that the limit of φk is π/2 as k grows. This allows us to construct centrally symmetric polytopes with a record number of faces.
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