# Article

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Keywords:
isometric foldings; edge-to-edge spherical tilings; homotopy
Summary:
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 $f_s(x,y,z)=(x,y,|z|)$.
References:
[1] Breda, A. M. d'Azevedo: {Isometric Foldings}. PhD Thesis, University of Southampton, U.K. (1989).
[2] Breda, A. M. d'Azevedo: {A class of tilings of $S^2$}. Geometriae Dedicata 44 (1992), 241-253. MR 1193117
[3] Breda, A. M. d'Azevedo, Santos, A. F.: Dihedral $f$-tilings of the sphere by spherical triangles and equiangular well centered quadrangles. Beiträge Algebra Geometrie 45 (2004), 447-461. MR 2093177
[4] Breda, A. M. d'Azevedo, Santos, A. F.: Dihedral $f$-tilings of the sphere by rhombi and triangles. Discrete Math. Theoretical Computer Sci. 7 (2005), 123-140. MR 2164062
[5] Breda, A. M. d'Azevedo, Santos, A. F.: {Dihedral $f$-tilings of the sphere by triangles and well centered quadrangles}. Hiroshima Math. J. 36 (2006), 235-288. DOI 10.32917/hmj/1166642302 | MR 2259739
[6] Hirsch, M.: {Differential Topology}. Graduate Texts in Math, 33 Springer-Verlag, New York (1976). MR 0448362 | Zbl 0356.57001
[7] Robertson, S. A.: {Isometric folding of riemannian manifolds}. Proc. Royal Soc. Edinb. Sect. A 79 (1977), 275-284. MR 0487893 | Zbl 0418.53016

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