Geometrically Regular Handle-Bodies

Year: 2025 Authors: Carlo H. Séquin

Core claim

Geometrically regular shapes can be constructed beyond Platonic solids, including curved genus-zero forms and higher-genus handle-bodies with identical flags.

Topics

geometric regularity, handle-bodies, regular maps, knot embeddings

Domains

topological graph theory, polyhedral geometry, symmetry groups, genus surfaces, sculpture, 3D modeling, kinetic-looking forms, craft-inspired geometry

Methods

projection to circum-spheres, CAD modeling, Catmull-Clark subdivision, surface thickening

Media

balloon-like surfaces, 3D-printed models, crocheted trefoil, ribbon-country surfaces

Source status

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