Cohomology Groups for Spaces of Twelve-Fold Tilings

Abstract We consider tilings of the plane with twelve-fold symmetry obtained by cut-and-projection method. compute their cohomology groups using techniques introduced in [ 9]. To do this, we completely describe window, orbits lines under group action, and 0-singularities. The complete family generalized can be described two-parameters it presents a surprisingly rich cohomological structure. put this finding into perspective, one should compare our results five-fold (more commonly known as Penrose tilings). In case, form one-parameter family, which fits simply two types cohomology.