School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Document Type

Article

Publication Date

6-2-2021

Abstract

A closed piecewise linear curve is called integral if it is comprised of unit intervals. Kenyon's problem asks whether for every integral curve γ in ℝ3, there is a dome over γ, i.e. whether γ is a boundary of a polyhedral surface whose faces are equilateral triangles with unit edge lengths. First, we give an algebraic necessary condition when γ is a quadrilateral, thus giving a negative solution to Kenyon's problem in full generality. We then prove that domes exist over a dense set of integral curves. Finally, we give an explicit construction of domes over all regular n-gons.

Comments

Original published version available at https://doi.org/10.1093/imrn/rnab138

Publication Title

International Mathematics Research Notices

DOI

10.1093/imrn/rnab138

Plum Print visual indicator of research metrics
PlumX Metrics
  • Usage
    • Downloads: 41
    • Abstract Views: 3
  • Captures
    • Readers: 1
see details

Included in

Mathematics Commons

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.