Nihonkai Mathematical Journal

Notes on Vertex Atlas of Danzer Tiling

Hiroko Hayashi, Yuu Kawachi, Kazushi Komatsu, Aya Konda, Miho Kurozoe, Fumihiko Nakano, Naomi Odawara, Rika Onda, Akinobu Sugio, and Masatetsu Yamauchi

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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

Permanent link to this document
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]

Keywords
Quasiperiodic tiling substitution rule rotational symmetry

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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