Dirichlet Tessellations of a Plane by Congruent Quadrangles

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New Zealand Journal of Mathematics

Vol. 39, (2009), Pages 79-101


Yusuke Takeo

Division of Mathematics and Mathematical Science

Department of Computer Science and Engineering

Graduate School of Engineering,

Nagoya Institute of Technology

Gokiso

Nagoya, 466-8555

JAPAN

mailto:morgen1029@gmail.com

Toshiaki Adachi

Department of Mathematics

Nagoya Institute of Technology

Nagoya 466-8555

JAPAN

mailto:adachi@nitech.ac.jp




Abstract In this paper we give a necessary and sufficient condition for some tessellations of a plane \mathbb{R}^2 by congruent convex quadrangles to be Dirichlet.

Keywords Dirichlet tessellation, quadrangles, sites.

Classification (MSC2000) Primary: 52C20; Secondary: 05B45.

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