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I think this problem has been mentioned several times now, so maybe a more detailed elaboration would be nice. I honestly don't see how you can define any meaningful embedding in a space like, say, $\mathbb{Z}^{1,3}$. For one thing, any finite...
Questions for both your approaches (Leuenberger and Pasqua): Can you specify more clearly what edges and vertices your eventual graphs consist of? When you intertwine two grids, Leuenberger, what edges do you create? Or, Pasqua, what are the edges...
However, if hypergraphs are to be used extensively, it could be important to develop some more systematic, short-hand notation for it. Both when working with pen and paper and when working on a computer. (I don't know why my name is not shown in...