An n-fold groupoid is a natural generalization of the idea of a double groupoid. Starting from n simple groupoids with a common base of objects, it is possible to proceed inductively to arrive at the notion of an n-fold groupoid as a set \(\mathcal {Q}\) with n different groupoid structures, the base of each of which is an \((n-1)\) -fold groupoid. The elements of \(\mathcal {Q}\) can be regarded as hypercube skeletons. As expected, it is possible to define the material n-fold groupoid associated with a composite or a metamaterial of n constituents. Interestingly, the natural hierarchical structure of an n-skeleton can be interpreted physically in a composite in terms of the various sub-mixtures made up of all possible combinations of some of the constituents.