This article is
- freely available
Symmetry 2012, 4(3), 545-565; doi:10.3390/sym4030545
Department of Mathematics, Northeastern University, Boston, MA 02115, USA
Received: 29 June 2012; in revised form: 13 August 2012 / Accepted: 19 August 2012 / Published: 30 August 2012
(This article belongs to the Special Issue Polyhedra)
Download PDF Full-Text [355 KB, uploaded 30 August 2012 09:40 CEST]
Abstract: 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.
Keywords: tiling; pseudotiling; abstract polytope; realization
Article StatisticsClick here to load and display the download statistics.
Notes: Multiple requests from the same IP address are counted as one view.
MDPI and ACS Style
Leopold, U. Barrel Pseudotilings. Symmetry 2012, 4, 545-565.AMA Style
Leopold U. Barrel Pseudotilings. Symmetry. 2012; 4(3):545-565.Chicago/Turabian Style
Leopold, Undine. 2012. "Barrel Pseudotilings." Symmetry 4, no. 3: 545-565.