Geometric Criteria for Realizability of Tensegrities in Higher Dimensions

In this paper we study a classical Maxwell question on the existence of self-stresses for frameworks, which are called tensegrities. We give a complete answer on geometric conditions of at most $(d+1)$-valent tensegrities in $d$-dimensional space both in terms of discrete multiplicative 1-forms and in terms of “join” and “intersection” operations in projective geometry.

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