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Joan Taylor's Tilings

Cube tiling

Eve tiling and variants
Rhombus seed tilings
Square tilings
Triangle and 3-fold
symmetry tilings
Cross  & 3 key tiles
Eve to llama tiling
2 Squares tiling
Cube tiling
Cube 1
Cube 1    PDF 9.7MB
Cube 2
Cube 2    PDF 5.9MB
Cube 3
Cube 3   PDF 8.3MB
Cube 4
Cube 4    PDF 8.2MB
Cube 5
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)