Fold-and-Cut Lines for the Hat, Turtle, and Spectre Tiles

Year: 2025 Authors: David Richeson

Core claim

Using straight skeletons and perpendicular fold lines, the author constructs one-cut fold-and-cut patterns for the hat and turtle tiles and adapts the method for the spectre tile.

Topics

fold-and-cut theorem, aperiodic monotiles, flat-folding, crease pattern construction, straight skeleton

Domains

computational geometry, origami mathematics, graph theory, paper folding, geometric design, visual pattern making

Methods

straight skeleton algorithm, perpendicular line construction, mountain-valley assignment, ad hoc adjustment

Media

paper, crease patterns, supplemental printable templates

Source status

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