A lower bound theorem for $d$-polytopes with $2d+1$ vertices

Guillermo Pineda-Villavicencio, David Yost

Published 2021-02-25Version 1

We establish the exact lower bound for the number of $k$-faces of $d$-polytopes with $2d+1$ vertices, for each value of $k$, and characterise the minimisers. As a byproduct, we characterise all $d$-polytopes with $d+3$ vertices, and only one or two edges more than the minimum.