Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN (electronic): 1944-4184
ISSN (print): 1944-4176
Author index
To appear
Other MSP journals
Higher-dimensional origami constructions

Deveena R. Banerjee, Sara Chari and Adriana Salerno

Vol. 16 (2023), No. 2, 297–312

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.

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

Communicated by Vadim Ponomarenko
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