skeleton(n, Delta)
The $k$-skeleton of an abstract simplicial complex is the subcomplex consisting of all of the faces of dimension at most $k$. When the abstract simplicial complex is pure its $k$-skeleton is simply generated by its $k$-dimensional faces.
The boundary of the 4-simplex is a simplicial 3-sphere with 5 vertices, 5 facets, and a minimal nonface that corresponds to the interior of the sphere.
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The abstract simplicial complex from Example 1.8 of Miller-Sturmfels' Combinatorial Commutative Algebra consists of a triangle (on vertices $a$, $b$, $c$), two edges (connecting $c$ to $d$ and $b$ to $d$), and an isolated vertex (namely $e$). It has six minimal nonfaces. Moreover, its 1-skeleton and 2-skeleton are not pure.
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The source of this document is in SimplicialComplexes/Documentation.m2:1900:0.