A self-similar dodecagonal quasiperiodic tiling of the plane in terms of squares, regular hexagons and thin rhombi

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Abstract
The author presents a dodecagonal quasiperiodic tiling of the plane in terms of three kinds of tiles: a square, a regular hexagon and a thin rhombus whose acute inner angles are 30 degrees . The dodecagonal tiling is self-similar with respect to a dilatation by 2+ square root 3. It is associated with a dodecagonal quasiperiodic lattice which is obtained by a projection from a hyperhoneycomb lattice in four dimensions. The hyperhoneycomb lattice is a non-Bravais lattice composed of four Bravais sublattices and the author must assign 'windows' with different orientations to different sublattices. The author discusses in detail the relationships of the present method of obtaining a dodecagonal tiling to other methods.

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