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From: Walter Roberson on 18 May 2010 15:24
Bruno Luong wrote:

> The geodesic on polytope is a straight line when the polytope is
> flattenen (making a cuts on the cell edges, excepted those crossed by
> the geoderic, then change the dihedral angle between to neighboring
> faces to pi, i.e., 180 degree).

Yes, _conceptually_, if we were to take a model of the geometry in which we
replaced all of the faces with small rigid plates, and replaced all of the
edges with hinges, then if we were to pick up the model by the two points and
pull those points apart as far as they go (assuming no elasticity!), then the
geodesic would be the shortest path along the "top" (assuming the other pieces
will be pulled downwards by gravity.)
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