**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 + 2c`^{2} +
c^{3} + 2c^{5} + c^{7} = 1 and tiling signature
**001144**.

A third has the dissection equation `c +
c`^{2} + 3c^{3} + c^{4} + c^{5} = 1 and
tiling signature **001122**.

The fourth has the dissection equation `2c +
c`^{4} + 2c^{5} + c^{6} + c^{7}, and tiling
signature **003344**.

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

The second complex teragon has 8 derived tiles. Four have have dissection
equation `c + c`^{2} + 3c^{3} +
c^{4} + c^{5} = 1 and tiling signature **001122**.

Two have dissection equation `c + 2c`^{2} +
c^{3} + 2c^{5} + c^{7}, and tiling signature
**001144**.

and two have dissection equation `2c +
c`^{4} + 2c^{5} + c^{6} + c^{7}, and tiling
signature **003344**.

© 2017 Stewart R. Hinsley