Nihonkai Mathematical Journal

Notes on Vertex Atlas of Danzer Tiling

Abstract

In this note, we study in detail the remark in the appendix of Danzer [6]. We find that planer Danzer tilings have many different aspects than Penroze tilings. For e.g., we observe that Danzer tiling with 7-fold symmetry does not belong to the topological closure of tilings generated by up-down generation.

Article information

Source
Nihonkai Math. J., Volume 22, Number 1 (2011), 49-58.

Dates
First available in Project Euclid: 14 June 2012

https://projecteuclid.org/euclid.nihmj/1339694050

Mathematical Reviews number (MathSciNet)
MR2894025

Zentralblatt MATH identifier
1256.52009

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

Citation

Hayashi, Hiroko; Kawachi, Yuu; Komatsu, Kazushi; Konda, Aya; Kurozoe, Miho; Nakano, Fumihiko; Odawara, Naomi; Onda, Rika; Sugio, Akinobu; Yamauchi, Masatetsu. Notes on Vertex Atlas of Danzer Tiling. Nihonkai Math. J. 22 (2011), no. 1, 49--58. https://projecteuclid.org/euclid.nihmj/1339694050

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