Tiling the Euclidean and Hyperbolic planes with ribbons

Benedikt Kolbe; Vanessa Robins

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arXiv · 1904.03788

Tiling the Euclidean and Hyperbolic planes with ribbons

Benedikt Kolbe·Vanessa Robins

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Abstract

We describe a method to classify crystallographic tilings of the Euclidean and hyperbolic planes by tiles whose stabiliser group contains translation isometries or whose topology is not that of a closed disk. We tackle this problem from two different viewpoints, one with constructive techniques to enumerate such tilings and the other from a viewpoint of classification. The methods are purely topological and generalise Delaney-Dress combinatorial tiling theory. The classification is up to equivariant equivalence and is achieved by viewing tilings as decorations of orbifolds.

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Benedikt Kolbe, Vanessa Robins. 2019-04-08. Tiling the Euclidean and Hyperbolic planes with ribbons. https://arxiv.org/abs/1904.03788

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