Block Systems of Ranks 3 and 4 Toroidal Hypertopes

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dc.contributor.advisorWeiss, Asia Ivic
dc.creatorEns, Eric James Loepp
dc.date.accessioned2018-11-21T13:52:09Z
dc.date.available2018-11-21T13:52:09Z
dc.date.copyright2018-08-14
dc.date.issued2018-11-21
dc.date.updated2018-11-21T13:52:09Z
dc.degree.disciplineMathematics & Statistics
dc.degree.levelDoctoral
dc.degree.namePhD - Doctor of Philosophy
dc.description.abstractThis dissertation deals with abstract combinatorial structure of toroidal polytopes and toroidal hypertopes. Abstract polytopes are objects satisfying the main combinatorial properties of a classical (geometric) polytope. A regular toroidal polytope is an abstract polytope which can be constructed from the string affine Coxeter groups. A hypertope is a generalization of an abstract polytope, and a regular toroidal hypertope is a hypertope which can be constructed from any affine Coxeter group. In this thesis we classify the rank 4 regular toroidal hypertopes. We also seek to find all block systems on a set of (hyper)faces of toroidal polytopes and hypertopes of ranks 3 and 4 as well as the regular and chiral toroidal polytopes of ranks 3. A block system of a set X under the action of a group G is a partition of X which is invariant under the action of G.
dc.identifier.urihttp://hdl.handle.net/10315/35556
dc.language.isoen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectMathematics
dc.subject.keywordsRegularity
dc.subject.keywordsChirality
dc.subject.keywordsToroids
dc.subject.keywordsThin Geometries
dc.subject.keywordsHypermaps
dc.subject.keywordsAbstract Polytopes
dc.subject.keywordsBlock Systems
dc.subject.keywordsSystems of Imprimitivity
dc.subject.keywordsDiscrete Geometry
dc.subject.keywordsPolytopes
dc.subject.keywordsRegular Polytopes
dc.subject.keywordsToroidal Polytopes
dc.titleBlock Systems of Ranks 3 and 4 Toroidal Hypertopes
dc.typeElectronic Thesis or Dissertation

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