Barrel Pseudotilings

Symmetry

关键词: tiling;    pseudotiling;    abstract polytope;    realization;   

DOI  :  10.3390/sym4030545

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2012 by the authors; licensee MDPI, Basel, Switzerland.