# Is there a way to check if a given simplicial complex is a pseudomanifold with boundary?

Def: A pseudomanifold with boundary is a simplicial complex with the following properties: โข it is pure of some dimension ๐ (all of its facets are ๐-dimensional) โข every (๐ โ 1)-dimensional simplex is the face of at most two facets โข for every two facets ๐ and ๐ , there is a sequence of facets ๐ = ๐_0, ๐_1, ..., ๐_๐ = ๐ such that for each ๐, ๐_๐ and ๐_{๐โ1} intersect in a (๐ โ 1)-simplex