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

## Allodemisymmetric Tiles

As each order 3 tile has 9 potential legitimate order 7 partial post(allo)composition
derivatives and there are two order 3 demisymmetric tiles there are a
potential 18 order 7 allodemisymmetric tiles. However 7 of the attractors are
disconnected, reducing the number to 11.

For the first “external” tile there are 6 derived tiles. Two are
simple teragons with dissection equation `c +
c`^{2} + 3c^{3} + c^{4} + c^{5} = 1 and
tiling signature **001122** (demisymmetric tiles have two copies, tiling a
symmetric tile, in the unit cell).

The other four are complex teragons, two with dissection equation `c + c`^{2} + 3c^{3} + c^{4} +
c^{5} = 1 and tiling signature **001122**,

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

The other demisymmetric tile gives rise to 5 derived tiles. They are all
complex teragons.

There are three with with dissection equation `c +
c`^{2} + 3c^{3} + c^{4} + c^{5} = 1 and
tiling signature **001122**

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

© 2017 Stewart R. Hinsley