Is there an aperiodic tiling consisting of deformed hexagons? The typical Penrose tiling consists of two deformed quadrangles. But it's there any aperiodic tiling consisting entirely of two or more deformed hexagons? Maybe even one that shares some properties of a hexagonal tiling such as only edge-neighbours?

Yes. Use the Penrose Rhombus Tiling as a start. The edges with a round bump, use a straight line. Those with the triangle, use two lines.
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