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Visualization of Regular Maps: The Chase Continues.

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    IEEE Transactions on Visualization and Computer Graphics
    |September 11, 2015
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    Summary
    This summary is machine-generated.

    Researchers developed a new visualization method for regular maps, creating novel space models of symmetric tilings on surfaces. This technique generated approximately 45 new examples, including the genus 7 Hurwitz surface.

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    Area of Science:

    • Topology
    • Geometric Group Theory
    • Discrete Geometry

    Background:

    • Regular maps are symmetric tilings of surfaces where faces, vertices, and edges are indistinguishable.
    • Platonic solids are common examples, but regular maps also exist on higher-genus surfaces.

    Purpose of the Study:

    • To present a novel method for visualizing regular maps.
    • To generate new examples of regular maps and their corresponding space models.

    Main Methods:

    • Extending previous work, the new method matches regular maps with target shapes in the hyperbolic plane.
    • Target shapes are generated through operations like duplicating maps, merging triangles, creating holes, and edge gluing.

    Main Results:

    • The method successfully produced approximately 45 new regular map examples.
    • Notable among these is the genus 7 Hurwitz surface, a significant discovery in map enumeration.

    Conclusions:

    • The developed visualization technique expands the known catalog of regular maps.
    • This approach offers a powerful tool for exploring and understanding complex symmetric structures on surfaces.