A Tale of Centrally Symmetric Polytopes and Spheres

  • Isabella NovikEmail author
Part of the Association for Women in Mathematics Series book series (AWMS, volume 16)


This paper is a survey of recent advances as well as open problems in the study of face numbers of centrally symmetric simplicial polytopes and spheres. The topics discussed range from neighborliness of centrally symmetric polytopes and the Upper Bound Theorem for centrally symmetric simplicial spheres to the Generalized Lower Bound Theorem for centrally symmetric simplicial polytopes and the lower bound conjecture for centrally symmetric simplicial spheres and manifolds.



I am grateful to Steve Klee, Connor Sawaske, Hailun Zheng, Günter Ziegler, and the anonymous referee for numerous comments on the preliminary version of this paper.


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© The Author(s) and the Association for Women in Mathematics 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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