Next Article in Journal
On the Notions of Symmetry and Aperiodicity for Delone Sets
Next Article in Special Issue
Hexagonal Inflation Tilings and Planar Monotiles
Previous Article in Journal
A Higher Dimensional Description of the Structure of β-Mn
Previous Article in Special Issue
Superspheres: Intermediate Shapes between Spheres and Polyhedra
Article Menu

Export Article

Open AccessArticle
Symmetry 2012, 4(3), 545-565;

Barrel Pseudotilings

Department of Mathematics, Northeastern University, Boston, MA 02115, USA
Received: 29 June 2012 / Revised: 13 August 2012 / Accepted: 19 August 2012 / Published: 30 August 2012
(This article belongs to the Special Issue Polyhedra)
View Full-Text   |   Download PDF [355 KB, uploaded 30 August 2012]   |  


This paper describes 4-valent tiling-like structures, called pseudotilings, composed of barrel tiles and apeirogonal pseudotiles in Euclidean 3-space. These (frequently face-to-face) pseudotilings naturally rise in columns above 3-valent plane tilings by convex polygons, such that each column is occupied by stacked congruent barrel tiles or congruent apeirogonal pseudotiles. No physical space is occupied by the apeirogonal pseudotiles. Many interesting pseudotilings arise from plane tilings with high symmetry. As combinatorial structures, these are abstract polytopes of rank 4 with both finite and infinite 2-faces and facets. View Full-Text
Keywords: tiling; pseudotiling; abstract polytope; realization tiling; pseudotiling; abstract polytope; realization

Figure 1

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Share & Cite This Article

MDPI and ACS Style

Leopold, U. Barrel Pseudotilings. Symmetry 2012, 4, 545-565.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top