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Higher-dimensional origami constructions

Deveena R. Banerjee, Sara Chari and Adriana Salerno

Vol. 16 (2023), No. 2, 297–312
Abstract

Origami is an ancient art that continues to yield both artistic and scientific insights to this day. In 2012, Buhler, Butler, de Launey, and Graham extended these ideas even further by developing a mathematical construction inspired by origami — one in which we iteratively construct points on the complex plane (the “paper”) from a set of starting points (or “seed points”) and lines through those points with prescribed angles (or the allowable “folds” on our paper). Any two lines with these prescribed angles through the seed points that intersect generate a new point, and by iterating this process for each pair of points formed, we generate a subset of the complex plane. We extend previously known results about the algebraic and geometric structure of these sets to higher dimensions. In the case when the set obtained is a lattice, we explore the relationship between the set of angles and the generators of the lattice and determine how introducing a new angle alters the lattice.

Keywords
origami construction, lattice
Mathematical Subject Classification
Primary: 06B99
Milestones
Received: 1 February 2022
Revised: 26 May 2022
Accepted: 31 May 2022
Published: 26 May 2023

Communicated by Vadim Ponomarenko
Authors
Deveena R. Banerjee
Department of Molecular Physiology and Biophysics
Vanderbilt University
Nashville, TN
United States
Sara Chari
Department of Mathematics
Bates College
Lewiston, ME
United States
Adriana Salerno
Department of Mathematics
Bates College
Lewiston, ME
United States