A graph has a flexible assignment of spherical edge lengths if and only if it admits a NAP-coloring, and K3,3 has exactly three proper spherical motions: two Dixon-type motions and one new constant diagonal angle motion.
Counting realizations of Laman graphs on the sphere
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
We present an algorithm that computes the number of realizations of a Laman graph on a sphere for a general choice of the angles between the vertices. The algorithm is based on the interpretation of such a realization as a point in the moduli space of stable curves of genus zero with marked points, and on the explicit description, due to Keel, of the Chow ring of this space.
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On the existence of paradoxical motions of generically rigid graphs on the sphere
A graph has a flexible assignment of spherical edge lengths if and only if it admits a NAP-coloring, and K3,3 has exactly three proper spherical motions: two Dixon-type motions and one new constant diagonal angle motion.