On periodically-cyclic Gale 4-polytopes
نویسندگان
چکیده
منابع مشابه
A Construction for Periodically-Cyclic Gale 2m-Polytopes
For each v, k and m such that v ≥ k ≥ 2m + 2 ≥ 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. MSC 2000: 52B11, 52B05
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A remarkable result of I. Shemer [4] states that the combinatorial structure of a neighbourly 2m-polytope determines the combinatorial structure of each of its subpolytopes. From this, it follows that every subpolytope of a cyclic 2m-polytope is cyclic. In this note, we present a direct proof of this consequence that also yields that certain subpolytopes of a cyclic (2m+ 1)-polytope are cyclic.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2001
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00112-1