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On deformations of spherical isometric foldings

Ana M. BredaAltino F. Santos — 2010

Czechoslovak Mathematical Journal

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 spherical isometric folding f s defined by f s ( x , y , z ) = ( x , y , | z | ) .

Geometric and combinatorial structure of a class of spherical folding tessellations – I

Catarina P. AvelinoAltino F. Santos — 2017

Czechoslovak Mathematical Journal

A classification of dihedral folding tessellations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent four papers by Avelino and Santos (2012, 2013, 2014 and 2015). In this paper we extend this classification, presenting all dihedral folding tessellations of the sphere by kites and scalene triangles in which the shorter side of the kite is equal to the longest side of the triangle. Within two possible cases of adjacency, only one will be addressed....

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