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This is a somewhat fuzzy question, so I will try my best to give a formulation which includes everything relevant while excluding everything else. I would like to find out if anyone else has studied ...

Let us fix $\Delta$ a finite simplicial complex, and label the vertices of $\Delta$ as $\{1,2,\ldots,n\}$. For each $F\in \Delta$ let us consider the point in $\mathbb{R}^n$ given by: $$e_F := \sum_{i\...