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FMF, Mathematical Library, Lj. (MAKLJ)
  • Petrie schemes
    Williams, Gordon Ian
    Petrie polygons, especially as they arise in the study of regular polytopes and Coxeter groups, have been studied by geometers and group theorists since the early part of the twentieth century. An ... open question is the determination of which polyhedra possess Petrie polygons that are simple closed curves. The current work explores combinatorial structures in abstract polytopes, called Petrie schemes, that generalize the notion of a Petrie polygon. It is established that all of the regular convex polytopes and honeycombs in Euclidean spaces, as well as all of the Grünbaum-Dress polyhedra, possess Petrie schemes that are not self-intersecting and thus have Petrie polygons that are simple closed curves. Partial results are obtained for several other classes of less symmetric polytopes.
    Source: Canadian journal of mathematics = Journal canadien de mathématiques. - ISSN 0008-414X (Vol. 57, no. 4, 2005, str. 844-870)
    Type of material - article, component part
    Publish date - 2005
    Language - english
    COBISS.SI-ID - 17595993

    Link(s):

    http://dx.doi.org/10.4153/CJM-2005-033-6

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