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

## Alloexternal Tiles

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

For the first “external” tile there are 3 derived tiles. One is a simple
teragon with dissection equation `c + c`^{2} +
3c^{3} + c^{4} + c^{5} = 1 and tiling signature
**012**.

The other two are complex teragons, also with dissection equation `c + c`^{2} + 3c^{3} + c^{4} +
c^{5} = 1 and tiling signature **012**.

The other “external” tile gives rise to 6 derived tiles. There are two
simple teragons, one with dissection equation `c +
c`^{2} + 3c^{3} + c^{4} + c^{5} = 1 and
tiling signature **012**, and the other with disssection equation `2c + 2c`^{4} + 2c^{7} + c^{9} =
1 and tiling signature **036**.

There are four complex teragons. Three have dissection equation `c + c`^{2} + 3c^{3} + c^{4} +
c^{5} = 1 and tiling signature **012**, and the other with
dissection equation `c + 2c`^{2} +
c^{3} + 2c^{5} + c^{7} = 1 and tiling signature
**014**.

© 2017 Stewart R. Hinsley