Curved Crease Folds of Spherical Polyhedra with Regular Faces

Year: 2019 Authors: Klara Mundilova

Core claim

A family of single-sheet curved crease folds can realize spherical polyhedra with regular faces, including the five Platonic solids, via explicit cylinder-cone constructions.

Topics

curved crease origami, spherical polyhedra, developable surfaces, Platonic solids

Domains

geometry, differential geometry, parametrization, developable surfaces, origami, paper folding, mathematical art, generative form

Methods

cylinder-cone construction, crease-curve parametrization, isometry condition, surface reflection

Media

single sheet of paper, cylinders, cones, developed paper patches

Source status

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