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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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

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

First available in Project Euclid: 14 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Quasiperiodic tiling substitution rule rotational symmetry


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.

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