Helical Petrie Polygons

Year: 2016 Authors: Paul Gailiunas

Core claim

Petrie polygons of regular sponges can be represented as circular helices and continuously transformed through dual configurations, revealing intermediate forms and new helix arrangements.

Topics

Petrie polygons, regular sponges, dual polyhedra, helical paths

Domains

polyhedral geometry, topology, geometric symmetry, mathematical art, architectural geometry, pattern design

Methods

geometric definition, dual correspondence, continuous transformation, visual comparison

Media

polyhedral packings, saddle surfaces, circular helices, triply periodic minimal surfaces

Source status

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