Chaim's Cubic PV

Discovered by


Part of an infinite series, where most tilings in this series are not flc, this one is the exception. The reason is that the inflation factor is a - real - PV number. By an argument in [PR] this forces flc. Interestingly, the shape of the tiles can vary. That is, there is one free parameter $l$ , $0 < l < 1+s$, and the smallest prototile is the triangle with sides $1,s,l$ ($s$ the largest root of $x^{3}-x-1$). In particular, one can have obtuse triangles, as well as rectangular ones or acute ones as prototiles.

Substitution Rule

Rule Chaim's Cubic PV


Patch Chaim's Cubic PV


Priebe-Frank, N and Robinson, E A jr
Generalized beta-expansions, substitution tilings, and local finiteness
preprint A0506098