Circle Packings From Tilings Of The Plane

Authors

Philip Rehwinkel , '22
Ian Whitehead, Swarthmore CollegeFollow
David Yang , '24
Mengyuan Yang , '25

Document Type

Article

Publication Date

4-2024

Published In

Journal Of Geometry

Abstract

We introduce a new class of fractal circle packings in the plane, generalizing the polyhedral packings defined by Kontorovich and Nakamura. The existence and uniqueness of these packings are guaranteed by infinite versions of the Koebe–Andreev–Thurston theorem. We prove structure theorems giving a complete description of the symmetry groups for these packings. And we give several examples to illustrate their number-theoretic and group-theoretic significance.

Keywords

Circle packing, Apollonian packing, Polyhedral packing, Koebe–Andreev–Thurston theorem

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Comments

This work is freely available under a Creative Commons license.

Recommended Citation

Philip Rehwinkel , '22; Ian Whitehead; David Yang , '24; and Mengyuan Yang , '25. (2024). "Circle Packings From Tilings Of The Plane". Journal Of Geometry. Volume 115, Issue 1. DOI: 10.1007/s00022-024-00715-8
https://works.swarthmore.edu/fac-math-stat/325