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isometric foldings; edge-to-edge spherical tilings; homotopy
The behavior of special classes of isometric foldings of the Riemannian sphere $S^2$ under the action of angular conformal deformations is considered. It is shown that within these classes any isometric folding is continuously deformable into the {\it standard} spherical isometric folding $f_s$ defined by $f_s(x,y,z)=(x,y,|z|)$.
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