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Geometric and combinatorial structure of a class of spherical folding tessellations – I
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 4, pp. 891-918 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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. The combinatorial structure of each tiling is also analysed.
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. The combinatorial structure of each tiling is also analysed.
DOI : 10.21136/CMJ.2017.0610-15
Classification : 20B35, 52B05, 52C20
Keywords: dihedral f-tiling; combinatorial propertie; spherical trigonometry; symmetry group 
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Avelino, Catarina P.; Santos, Altino F. Geometric and combinatorial structure of a class of spherical folding tessellations – I. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 4, pp. 891-918. doi: 10.21136/CMJ.2017.0610-15

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