penrose-tiling-rhombi_002

3D Model

This is my 3D dimetric* interpretation of the below Penrose aperiodic tiling P3.

My brain usually trained to see isometric cubes shapes in hexagon-based patterns with 30°/60° angles can’t help but try to also see some in patterns for which it is less obvious like that one based on 72° angles (five-fold symmetry), so this far-fetched interpretation of mine is a structure where, unlike in the Wieringa roof, the rhombi are not congruent but a majority (about ⅔) of them are actually rectangles including many squares. See here geogebra.org/m/zccvjdj8 my calculations (done afterwards since I managed to create the model using simply visual cues) for the proportions and angles required for the 5 first faces at the center that can then be duplicated and moved to create the others.

*Requiered camera pitch angle is asin(tan(18°)) ≈ 18.961° for this dimetric view instead of ≈ 35.264° for standard isometric view.