From acute sets to centrally symmetric $2$-neighborly polytopes

TL;DR

This paper investigates the maximum number of vertices in centrally symmetric 2-neighborly polytopes, providing new bounds and explicit constructions that improve previous known limits.

Contribution

The authors present an explicit construction of centrally symmetric 2-neighborly polytopes with at least 2^{d-1}+2 vertices, advancing the understanding of their maximum size.

Findings

Maximum vertices are at least 2^{d-1}+2 for such polytopes.

Upper bound on vertices is 2^d.

Explicit construction demonstrates the lower bound.

Abstract

What is the maximum number of vertices that a centrally symmetric 2-neighborly polytope of dimension $d$ can have? It is known that the answer does not exceed $2^d$. Here we provide an explicit construction showing that it is at least $2^{d-1}+2$.