We propose a new programming control structure called ''multifor'', allowing to take advantage of parallelization models that were not naturally attainable with the polytope model before. In a multifor-loop, several loops whose bodies are run simultaneously can be defined. Respective iteration domains are mapped onto each other according to a run frequency -- the grain -- and a relative position -- the offset --. Execution models like dataflow, stencil computations or MapReduce can be represented onto one referential iteration domain, while still exhibiting traditional polyhedral code analysis and transformation opportunities. Moreover, this construct provides ways to naturally exploit hybrid parallelization models, thus significantly improving parallelization opportunities in the multicore era. Traditional polyhedral software tools are used to generate the corresponding code. Additionally, a promising perspective related to non-linear mapping of iteration spaces is also presented, yielding to run a loop nest inside any other one by solving the problem of inverting "ranking Ehrhart polynomials".