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I am writing some code to generate a Vietoris-Rips complex given a set of data points. The VR complex is generated from 0-complexes, 1-complexes, 2-complex, etc., where $k+1$ represents the number of points in the complex. I have seen VR complexes go up to about 2-complexes but not beyond that. I was wondering if there is any consensus on how high to set $k$. I am asking because it seems difficult to visualize complexes of dimension higher 2 since it is hard to represent higher complexes using the standard face and edge colorings of a network diagram.

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Seems like most analyses rely on the 0, 1, and 2-simplices. The Vietoris-Rips complex just relies on 1-complexes, as does the Alpha complex. The 2-simplices help to visualize Cech complexes and to better see the holes that emerge in the complex. But otherwise, there does not seem to be a need to go beyond 2-simplices.

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