Infinite Families of Hypertopes from Centrally Symmetric Polytopes

Abstract

We construct infinite families of abstract regular polytopes of Schläfli type $\{4,p_1,\ldots,p_{n-1}\}$ from extensions of centrally symmetric spherical abstract regular $n$-polytopes. In addition, by applying the halving operation, we obtain infinite families of both locally spherical and locally toroidal regular hypertopes of type $\left\{\genfrac{}{}{0pt}{}{p_1}{p_1},\ldots,p_{n-1}\right\}$.