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Assume that you are given a net of 6 squares. Is there a simple criterion (in terms of a few invariants that can be computed quickly) to tell whether it is the net of a cube?

More generally, when is an arbitrary net of faces the net of a solid?

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    what is a "net"? do you mean a planar graph drawn (topologically) on a sphere? or a graph that is topologically equivalent to the faces of a particular type of solid, with given edge lengths that are to be tested for consistency with geometric realization of the solid?2012-06-18
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    See http://www.onlinemathlearning.com/geometry-nets.html2017-01-04

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