Portraits of Groups II, Orientation Reversing Actions

Year: 2007 Authors: Jay Zimmerman

Core claim

Finite groups with orientation-reversing symmetries can be portrayed on genus-2 surfaces using hybrid triangle groups, yielding an explicit portrait for the order-48 group P48.

Topics

group portraits, orientation-reversing actions, genus-2 surfaces, hybrid triangle groups

Domains

finite group actions, triangle groups, Fuchsian groups, surface topology, mathematical visualization, diagrammatic representation, surface drawing, geometric art

Methods

group presentations, coset labeling, polygonal diagrams, surface models

Media

Geometer’s SketchPad, colored curves, plane drawings, genus-2 surface model

Source status

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