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dc.contributor.authorXu, Xi
dc.date.accessioned2019-04-15T19:22:38Z
dc.date.available2019-04-15T19:22:38Z
dc.date.issued2018
dc.identifier.otherW Thesis 1558
dc.identifier.urihttp://hdl.handle.net/11040/24564
dc.descriptioni, 72 leaves: color illustrations.
dc.descriptionIncludes bibliographical references: leaves 72.
dc.description.abstractThis thesis introduces perfect colorings and the systematic way of generating perfect colorings. We study the perfect colorings for designs whose symmetry groups are 2-dimensional Euclidean crystallographic groups. Two-dimensional Euclidean crys- tallographic groups are discrete subgroups of the isometry group of the Euclidean plane. We classify crystallographic groups by their ranks. Crystallographic groups of rank 0, rank 1, and rank 2 are explained with details and examples. Theorems that related to the number of perfect colorings for designs with crystallographic symmetry groups are constructed and proved.en_US
dc.description.tableofcontents1 Abstract – 2 Background – 2.1 Symmetry and symmetry group – 2.2 Metric space and isometry group – 2.3 Crystallographic groups – 3 Coloring and perfect coloring – 4 Perfect colorings of square, hexagon, and pentagon – 4.1 Perfect colorings of square – 4.2 Perfect colorings of hexagon – 4.3 Perfect colorings of pentagon – 5 Counting perfect colorings of a design with symmetry group D2n – 6 Frieze patterns and colorings – 6.1 Frieze groups and frieze patterns – 6.2 Colorings of frieze patterns – 6.3 Imposing D2n Symmetry on a colored frieze pattern – 7 Wallpaper Patterns and colorings – 7.1 Wallpaper groups and wallpaper patterns – 7.1.1 Wallpaper patterns with parallelogram unit cells – 7.1.2 Wallpaper patterns with rectangular unit cells – 7.1.3 Wallpaper patterns with rhombic unit cells – 7.1.4 Wallpaper patterns with square unit cells – 7.1.5 Wallpaper patterns with hexagonal unit cells – 7.2 Future work : Colorings of wallpaper patterns
dc.language.isoen_USen_US
dc.publisherWheaton College (MA).en_US
dc.subjectUndergraduate research.en_US
dc.subjectUndergraduate thesis.en_US
dc.subject.lcshSymmetry groups.
dc.subject.lcshCrystallography, Mathematical.
dc.subject.lcshGeometry.
dc.subject.lcshMathematics.
dc.subject.lcshColor.
dc.titlePerfect colorings of a design with 2-dimensional euclidean crystallographic symmetry group.en_US
dc.title.alternativeSpine label: Perfect colorings of a design with 2-dimensional euclidean crystallographic.
dc.typeThesisen_US


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