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Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 42, No. 1, pp. 89-101 (2001)
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A Construction for Periodically-Cyclic Gale $2m$-Polytopes

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T. Bisztriczky

Dept. of Mathematics, University of Calgary, Calgary, Canada T2N 1N4 e-mail: tbisztri@math.ucalgary.ca

**Abstract:** For each $v$, $k$ and $m$ such that $v\geq k\geq 2m+2\geq 8$, we construct 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 facets based upon a labelling (total ordering) of the vertices so that every subset of $k$ successive vertices generates a cyclic $2m$-polytope.

**Classification (MSC2000):** 52B11, 52B05

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