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With the rising significance of (∞, n)-categories, it is important to have easy-to-handle models for those and understand them as much as possible. In these talks we will discuss the model of n-complicial sets, and study how one can realize convenient representatives of strict n-categories, which encode universal indexing shapes for diagrams valued in (∞, n)-categories. We will focus on n = 2, for which more results are available, but keep an eye towards the general case. This is joint work with Viktoriya Ozornova.