**Some tiles associated with the 6th unit cubic Pisot number**

## Allowindowed Tiles

Each normal order 3 tile has 9 potential legitimate order 7 partial post(allo)composition
derivatives. However, as there are two distinct dissections of the windowed tile, this is increased to a potential 18
order 7 allodemisymmetric tiles. However 6 of the attractors are disconnected,
and 2 are alternative dissections of the same attractor, reducing the number to
11.

As the windowed tile is a complex teragon, all the derived tiles are complex
teragons.

For the first dissection tile there are 6 derived tiles. Four have the
dissection equation `c + c`^{2} +
3c^{3} + c^{4} + c^{5} = 1 and tiling signature
**001122**, **011223** or **012234**. (The windowed tile has
alternative tilings with signatures **00**, **01** and **02**.)

Two have dissection equation `2c + c`^{4} +
2c^{5} + c^{6} + c^{7}, and tiling signature
**003344**, **013445** or **023456**.

The second dissection also has 6 derived tiles. The first is the alternative
dissection of the first of the tiles above. Of the remainder two have
dissection equation `c + c`^{2} +
3c^{3} + c^{4} + c^{5} = 1 and tiling signature
**001122**, **011223** or **012234**.

One has dissection equation `c + 2c`^{2} +
c^{3} + 2c^{5} + c^{7}, and tiling signature
**001144**, **011245** or **012345**.

and two have dissection equation `2c +
c`^{4} + 2c^{5} + c^{6} + c^{7}, and tiling
signature **003344**, **013445** or **023456**.

The alternative unit cells are

© 2017 Stewart R. Hinsley