Laperriere, Christiane2013-11-072013-11-0720092009Source: Masters Abstracts International, Volume: 48-05, page: 3021.http://hdl.handle.net/10393/28269http://dx.doi.org/10.20381/ruor-19168We study the cut and projection method, which is a way to construct tilings. This construction leads to a minimal Zd -action on the Cantor set. In this thesis, we will focus our attention on two examples that we will describe in full details. the Fibonacci tiling on R and the octogonal tiling on R2 . For the octogonal tiling, we find small strictly positive cocycles for the minimal action on specific cones of Z2 .99 p.enMathematics.Thesis