Browsing by Author "Finbow-Singh, Wendy"

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    Low dimensional neighbourly polytopes
    (2004) Finbow-Singh, Wendy; Bisztriczky, Ted
    Semi-cyclic 4-polytopes were introduced in [12]. In Chapter 2, we present the results from this paper. In particular, a complete facial description of the semi-cyclic 4polytopes is given. The Gohberg-Markus-Hadwiger Covering Conjecture is verified for the corresponding class of dual semi-cyclic 4-polytopes. The neighbourly 5-polytopes with nine vertices are considered in Chapter 3. We show that there are at least one hundred, twenty-six neighbourly 5-polytopes with nine vertices. In particular, we show that there are exactly eight neighbourly 5polytopes with nine vertices and two universal vertices, there are exactly four neighbourly 5-polytopes with nine vertices, one universal vertex, and one cyclic vertex figure, there are at least twenty-nine neighbourly 5-polytopes with one universal vertex, and there are at least eighty-nine neighbourly 5-polytopes with no universal vertices. We give a complete combinatorial description of each polytope. The GohbergMarkus-Hadwiger Covering Conjecture is verified for the corresponding class of dual neighbourly 5-polytopes with nine vertices. In Chapter 4, the connection between the neighbourly 4-polytopes with eight vertices, the neighbourly 5-polytopes with nine vertices, and the neighbourly 6polytopes with ten vertices is examined.