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Deformation of f-tilings versus deformation of isometric foldings

Avelino, Catarina P.; Santos, Altino F.

International Journal of Mathematics, 23(9) (2012), 1-13

We present some relations between deformation of spherical isometric foldings and deformation of spherical f-tilings. The natural way to deform f-tilings is based on the Hausdorff metric on compact sets. It is conjectured that any f-tiling is (continuously) deformable in the standard f-tiling ?s = {(x, y, z) ? S2 : z = 0} and it is shown that the deformation of f-tilings does not induce a continuous deformation on its associated isometric foldings.