Bisztriczky, TedFinbow-Singh, Wendy2005-08-192005-08-1920040612935159http://hdl.handle.net/1880/42391Bibliography: p. 127-128Semi-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.ix, 450 leaves : ill. ; 30 cm.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.doctoral thesis10.11575/PRISM/17155AC1 .T484 2004 F485