If I understand my PL topology correctly (and please correct me if I don't), if $K$ is a $k-$complex and $n\ge 2k+2$, then any two PL embeddings $a,b\colon K\to \mathbb{R}^n$ are isotopic. Therefore, the regular neighborhoods of $a(K)$ and $b(K)$ are homeomorphic, and we can think about them as "the" regular neighborhood of $K$.

Is it possible to describe this regular neighborhood without reference to a particular embedding? For instance, if $K$ is a manifold, then the regular neighborhood is homeomorphic to a product $K\times \mathbb{R}^{n-k}$, and I'd like something similar for complexes that aren't manifolds.