A polygonal version of Kenyon (1,2,1). The boundary is generated by the morphism $a \to b, b \to c, c \to c a' b' b'$ (where $x'$ is the inverse of $x$).
[Ken96]
Kenyon, Richard
The construction of self-similar tilings
Geom. Funct. Anal.
1996,
6, 3,
pp. 471--488,
MR1392326