Doing the Jitterbug with Islamic geometric patterns

Abstract

Vertex-to-vertex polyhedral jitterbug transformations provide for the creation of polyhedra with specific angular conditions at the vertices that facilitate regions of local symmetry that are atypical of the spherical geometry associated with the Platonic and Archimedean polyhedra. This allows for the introduction of unexpected Islamic geometric designs comprised of primary stars with n-fold rotational symmetry that would not otherwise conveniently cover the surface of the sphere; for example, the regular distribution of twelve 7-pointed stars. These three-dimensional jitterbug transformations have two-dimensional corollaries that are instructive in understanding this design process. This expands upon the historical use among some Muslim cultures of polyhedral geometry as an organizing principle for placing geometric patterns onto the surfaces of domes and domical niches, and provides contemporary artists with a new approach to applying geometric design onto spherical surfaces.

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