Exploring the Projective Plane via Variations on the Faceted Octahedron

Year: 2012 Authors: Frank Gould; S. Louise Gould

Core claim

A faceted octahedron can be reconfigured into a smooth projective-plane immersion in 3-space by introducing loops that remove singular obstructions.

Topics

projective plane, smooth immersion, faceted octahedron, triple point, topological visualization

Domains

topology, 3-manifold geometry, polyhedral geometry, surface immersions, fabric model, mathematical craft, visualization, polyhedral design

Methods

fabric construction, net development, virtual deformation, polyhedral reconfiguration

Media

stiff non-elastic fabric, zippers, Mathematica files, polyhedral nets

Source status

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