Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 42, No. 1, pp. 89-101 (2001)

A Construction for Periodically-Cyclic Gale $2m$-Polytopes

T. Bisztriczky

Dept. of Mathematics, University of Calgary, Calgary, Canada T2N 1N4 e-mail:

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

Full text of the article:

[Previous Article] [Next Article] [Contents of this Number]
© 2000 ELibM for the EMIS Electronic Edition