| 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 |
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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) |