Mimetic spectral element methods are arbitrary order methods which aim to mimic the underlying physical structure of a PDE. This is best accomplished in terms of differential geometry in which the physical variables are considered as differential k-forms. At the discrete level, the system is represented by k-cochains from algebraic topology. The map from k-forms to k-cochains is the generic DeRham map. There is more freedom in the map from k-cochains to k-forms, the so-called Whitney map. It is here that the higher order basis functions emerge.