A construction for periodically-cyclic Gale \(2m\)-polytopes (Q1591748)

For each \(v\), \(k\), and \(m\) such that \(v\geq k \geq 2m + 2 \geq 8\), the author constructs a periodically-cyclic Gale \(2m\)-polytope with \(v\) vertices and the period \(k\). For such a polytope, there is a complete description of each of its faces based upon a labelling (total ordering) of the vertices so that every subset of \(k\) successive vertices generates a cyclic \(2m\)-polytope. Note that motivation for this paper may be described as practical, theoretical and exploratory.