Local pattern mining on attributed graphs aims to detect subsets of vertices that are induced by patterns composed of specific sets of attributes. This paper generalizes such graph-based approaches to simplicial complexes building on the MinerLSD algorithm for efficient local pattern mining. We present according generalizations of the graph-based closed pattern case to simplicial complexes, as well as a generalization of the Modularity for simplicial complexes for creating such a higher-order pattern mining approach. We demonstrate the advantages of the proposed strategy via experimentation using several datasets.