## Hiroshima Mathematical Journal

### Strongly nonperiodic hyperbolic tilings using single vertex configuration

#### Abstract

A strongly nonperiodic tiling is defined as a tiling that does not admit infinite cyclic symmetry. The purpose of this article is to construct, up to isomorphism, uncountably many strongly nonperiodic hyperbolic tilings with a single vertex configuration by a hyperbolic rhombus tile. We use a tile found by Margulis and Mozes [5], which admits tilings, but no tiling with a compact fundamental domain.

#### Article information

Source
Hiroshima Math. J., Volume 48, Number 2 (2018), 133-140.

Dates
Received: 29 February 2016
Revised: 22 October 2017
First available in Project Euclid: 1 August 2018

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1533088825

Digital Object Identifier
doi:10.32917/hmj/1533088825

Mathematical Reviews number (MathSciNet)
MR3835553

Zentralblatt MATH identifier
06965537

Subjects
Primary: 52C23: Quasicrystals, aperiodic tilings
Secondary: 52C20: Tilings in $2$ dimensions [See also 05B45, 51M20]

#### Citation

Ahara, Kazushi; Akiyama, Shigeki; Hayashi, Hiroko; Komatsu, Kazushi. Strongly nonperiodic hyperbolic tilings using single vertex configuration. Hiroshima Math. J. 48 (2018), no. 2, 133--140. doi:10.32917/hmj/1533088825. https://projecteuclid.org/euclid.hmj/1533088825