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

## An Additional Order
5 Tile

It is likely that there are several order 5 tiles in addition to the order 5
dissections of the 8 order 3 tiles and the additional 58 order 5 tiles that can
be derived from the order 3 tiles. However order 5 tiles are harder to find
than order 3 tiles and I have only identified a single such tile.

An example IFS for this tile is `{ `**p** →
-ap + 1; p → -a^{2}p^{}; p → a^{2}p + 1; p
→ -a^{3}p + 1; p → a^{4}p + 1 }

There is an alternative dissection - the right hand 4 elements can be
rotated by 180° around their common centre.

It can be seen that those 4 elements form a symmetric tile, and hence that
this tile has a periodic tiling of the plane with unit cell signature
**0123**. The unit cell transforms are `{ `**p**
→ **p**; **p** → -a**p**; **p** →
a^{2}**p**; **p** → -a^{3}**p** }.

© 2017 Stewart R. Hinsley