Joan Taylor's Tilings

Cube tiling

Cube 1 PDF 9.7MB

Cube 2 PDF 5.9MB

Cube 3 PDF 8.3MB

Cube 4 PDF 8.2MB

Cube 5 PDF 5.6MB

To see a bigger image left click on the small image. To obtain a high definition image left click on "PDF" below the small image.

The single hexagonal tiling or llama tiling was given a 3D version by Josh Socolar which had a translational symmetry in the third dimension. This inspired me to try the several square tilings I had as decorations on the surfaces of a cube. The 2 Square tiling was the only one that worked. Unfortunately it has a translational symmetry in the (1,1,1) direction despite having all 6 planes involving the faces of any cube comprised of non-periodic 2D tilings. So it is not an aperiodic monotile. A 5 page pdf file of the description of this 3D tiling by shape-alone cubes is available here. (42KB)