Vertex-transitive monocoronal tilings from isohedral tilings

Symmetries of Monocoronal Tilings

Intricate Isohedral Tilings of 3D Euclidean Space

Various methods to create intricate tilings of 3D space are presented. They include modulated extrusions of 2D Escher tilings, free-form deformations of the fundamental domain of various 3D symmetry groups, highly symmetrical polyhedral toroids of genus 1, higher-genus cage structures derived from the cubic lattice as well as from the diamond and triamond lattices, and finally interlinked tiles...

Interlinked Isohedral Tilings of 3D Space

Di erent isohedral tilings of the Euclidian Space are studied in this paper. Using the Voronoi zone in various lattices, we derived toroidal shapes that interlink with each other to ll space completely. The tile of main interest was the 3-segment ring-tile, for which we found several linear approximations.

Hexagonal Parquet Tilings k - Isohedral Monotiles with Arbitrarily Large k

The interplay between local constraints and global structure of mathematical and physical systems is both subtle and important. The macroscopic physical properties of a system depend heavily on its global symmetries, but these are often difficult to predict given only information about local interactions between the components. A rich history of work on tilings of the Euclidean plane and higher...

Transitive triangle tilings in oriented graphs

In this paper, we prove an analogue of Corrádi and Hajnal's result. There exists n 0 such that for every n ∈ 3Z when n ≥ n 0 the following holds. If G is an oriented graph on n vertices and δ 0 (G) ≥ 7n/18, then G contains a perfect T T 3-tiling, which is a collection of vertex disjoint transitive triangles covering every vertex of G. This result is best possible, as there exists an oriented gr...