Smoothness of a polytope

Question

This might a bit a too general question to ask but I cannot get my head around this definition I found. A polytope $P\subset\mathbb{R}^n$ is smooth at the vertex if the set $ \{ (w_1-p),(w_2-p),...,(w_n-p)\}$ can be extended to a basis for $\mathbb{Z}^n$. Where do the $w_i$ come from? I understand that they are some vectors by which the set of points should form a base but no word whether the $w_i$ are arbitrary or not. If anyone could give me an explanation or better a concise definition I would be most thankful.