Infinite families of hypertopes from centrally symmetric polytopes

Abstract

We construct infinite families of abstract regular polytopes of type $\{4,p_1,\dots ,p_{n-1}\}$ 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 $\left\{\genfrac{}{}{0ex}{}{p_1}{p_1},\dots ,p_{n-1}\right\}$.

17 pages