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Dihedral symmetry

Marko Glavan (2017) Dihedral symmetry. Diploma thesis.

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    Abstract

    In this BCs thesis we describe the dihedral group, its structure and properties, and find certain objects which have dihedral symmetry. Dihedral group is one of the simplest finite groups. Since it is non-commutative, the structure of subgroups of the dihedral group is more interesting than that of the cyclic group. Before introducing the concept of the dihedral group, we make a short review of the basic notions from group theory and from the euclidean geometry that will be used in the thesis. Then we define the dihedral group as the group of isometries of the euclidean plane which preserve a regular $n$-gon. We list all its elements and classify them into conjugacy classes. We also find an abstract characterization of the dihedral group and examine the structure of its subgroups. To conclude, we list some concrete mathematical and non-mathematical objects which have dihedral symmetry.

    Item Type: Thesis (Diploma thesis)
    Keywords: group, regular n-gon, isometry, reflection, rotation, dihedral group, dihedral symmetry
    Number of Pages: 37
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    doc. dr. Boštjan KuzmanMentor
    asist. dr. Eva HorvatComentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=11711561)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 4687
    Date Deposited: 19 Sep 2017 15:59
    Last Modified: 19 Sep 2017 15:59
    URI: http://pefprints.pef.uni-lj.si/id/eprint/4687

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