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For $x=(x_1,...,x_n)\in \mathbb{R}^n$, let $Q_x=(x_1,x_1+1)\times ...\times (x_n,x_n+1)$ - the open cube having $x$ in its "bottom left" corner. It seems, I can prove (see a draft here) the following ...

Shellability of simplicial balls and spheres (simplicial complexes whose geometric realizations are homeomorphic to balls and spheres) has been studied quite extensively. There are many explicit ...