A Centrally Symmetric Version of the Cyclic Polytope

@article{Barvinok2008ACS,
title={A Centrally Symmetric Version of the Cyclic Polytope},
author={Alexander I. Barvinok and Isabella Novik},
journal={Discrete & Computational Geometry},
year={2008},
volume={39},
pages={76-99}
}

We define a centrally symmetric analogue of the cyclic polytope and study its facial structure. We conjecture that our polytopes provide asymptotically the largest number of faces in all dimensions among all centrally symmetric polytopes with n vertices of a given even dimension d = 2k when d is fixed and n grows. For a fixed even dimension d = 2k and an integer 1 ≤ j < k we prove that the maximum possible number of j-dimensional faces of a centrally symmetric d-dimensional polytope with n… CONTINUE READING