Some tiles associated with the 6th unit cubic Pisot number

Allocomplex Tiles

There are 3 complex teragons among the order 3 sixth cubic tiles, one of which is the windowed tile. As a normal order 3 tile has 9 potential legitimate order 7 partial post(allo)composition derivatives, the remaining two have a potential 18 order 7 allodemisymmetric tiles. However 7 of the attractors are disconnected reducing the number to 11.

As the base tiles are complex teragons, all the derived tiles are complex teragons.

For the first complex tile there are 4 derived tiles. Two have the dissection equation c + 2c2 + c3 + 2c5 + c7 = 1 and tiling signature 001144.

allocomplex tileallocomplex tile unit cell

allocomplex tileallocomplex tile unit cell

A third has the dissection equation c + c2 + 3c3 + c4 + c5 = 1 and tiling signature 001122.

allocomplex tileallocomplex tile unit cell

The fourth has the dissection equation 2c + c4 + 2c5 + c6 + c7, and tiling signature 003344.

allocomplex tileallocomplex tile unit cell

As this first complex teragon has two alternative unit cells these four derived tiles also have alternative unit cells.

allocomplex tileallocomplex tile unit cell allocomplex tileallocomplex tile unit cell

The second complex teragon has 8 derived tiles. Four have have dissection equation c + c2 + 3c3 + c4 + c5 = 1 and tiling signature 001122.

allocomplex tileallocomplex tile unit cell

allocomplex tileallocomplex tile unit cell

allocomplex tileallocomplex tile unit cell

allocomplex tileallocomplex tile unit cell

Two have dissection equation c + 2c2 + c3 + 2c5 + c7, and tiling signature 001144.

allocomplex tileallocomplex tile unit cell

allocomplex tileallocomplex tile unit cell

and two have dissection equation 2c + c4 + 2c5 + c6 + c7, and tiling signature 003344.

allocomplex tileallocomplex tile unit cell

allocomplex tileallocomplex tile unit cell

© 2017 Stewart R. Hinsley