Inspired by Snowflakes: Constructing, Folding and Cutting Regular Paper Polygons to Create Art with Dihedral Symmetry

Gwen L. Fisher and Nicole Silkton
Bridges: Mathematical Connections in Art, Music, and Science (2004)
Pages 195–202

Abstract

The structure of natural snowflakes can be abstracted mathematically and can be reproduced in paper and fabric art. Mathematically, natural snowflakes are beautiful examples of objects with a combination of both rotation symmetry and reflection symmetry, known as dihedral symmetry. Designs with dihedral symmetry can be easily constructed from regular polygons; so we provide a brief summary of the classic methods for constructing regular polygons including Euclidean constructions (compass and straightedge), paper folding constructions, as well as a practical method that uses a protractor. Finally, we provide several examples of how artists can use regular polygons made from paper to produce art with dihedral symmetry.

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