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Spherical and planar folding tessellations by kites and equilateral triangles

Avelino, Catarina P.; Santos, Altino F.

Australasian Journal of Combinatorics, 53 (2012), 109-125

We prove that there is a unique folding tessellation of the sphere and an infinite family of folding tessellations of the plane with prototiles a kite and an equilateral triangle. Each tiling of this family is obtained by successive gluing of two patterns composed of triangles and kites, respectively. The combinatorial structure and the symmetry group is achieved.