In terms of the design of the ‘mechanics’ of the tile system, the original tile shape was developed from playing around with hexagon dissections, part of a lesson developed for high school students.
There are surprisingly many ways to slice a hexagon up into identical pieces and many of these shapes that are created have interesting properties.
The tile shape chosen was found to be interesting because it was in essence both natural and unnatural in its formation. Although the 2 lines of symmetry chosen for the dissection are part of a regular Hexagon’s symmetry, each is from a different subset, which taken together forms a ninety degree angle which is in effect more of an imposition of a square’s symmetry onto that of the regular hexagon.
Scaling a tile using more tiles...
Moreover these tiles are what are known as ‘rep-tiles’: meaning that they can be placed together to form scaled copies of themselves, so, in theory, since the tiles are a dissection set from a hexagon, larger and larger hexagons should be able to be formed from them, which is indeed the case.