As well as showing that there are substitution rules with any Perron
inflation factor, in [Ken96]
, R. Kenyon
gives an explicit construction for the Perron numbers that satsify:
`$xn - a xn-1 + b x + c$`

, where `$a, b$,`

and `$c$`

are natural numbers.
This is an example of that method given in that paper.
A locally isomorphic version with polygonal tiles is Kenyon (1,2,1) Polygon.

[Ken96]

Kenyon, Richard

**The construction of self-similar tilings**

*Geom. Funct. Anal.*
1996,
6, 3,
pp. 471--488,
MR1392326