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Tilings of the sphere with right triangles I: The asymptotically right families
 ELECTRON J. COMBIN
, 2006
"... Sommerville [10] and Davies [2] classified the spherical triangles that can tile the sphere in an edgetoedge fashion. Relaxing this condition yields other triangles, which tile the sphere but have some tiles intersecting in partial edges. This paper determines which right spherical triangles withi ..."
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Sommerville [10] and Davies [2] classified the spherical triangles that can tile the sphere in an edgetoedge fashion. Relaxing this condition yields other triangles, which tile the sphere but have some tiles intersecting in partial edges. This paper determines which right spherical triangles within certain families can tile the sphere.
Spherical FTilings by Triangles and rSided Regular Polygons, r ≥ 5
, 2008
"... The study of dihedral ftilings of the sphere S² by spherical triangles and equiangular spherical quadrangles (which includes the case of 4sided regular polygons) was presented in [3]. Also, in [6], the study of dihedral ftilings of S² whose prototiles are an equilateral triangle (a 3sided regula ..."
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Cited by 3 (3 self)
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The study of dihedral ftilings of the sphere S² by spherical triangles and equiangular spherical quadrangles (which includes the case of 4sided regular polygons) was presented in [3]. Also, in [6], the study of dihedral ftilings of S² whose prototiles are an equilateral triangle (a 3sided regular polygon) and an isosceles triangle was described (we believe that the analysis considering scalene triangles as the prototiles will lead to a wide family of ftilings). In this paper we extend these results, presenting the study of dihedral ftilings by spherical triangles and rsided regular polygons, for any r ≥ 5. The combinatorial structure, including the symmetry group of each tiling, is given in Table 1.
CLASSIFICATION OF SPHERICAL TILINGS BY CONGRUENT QUADRANGLES OVER PSEUDODOUBLE WHEELS (I)  A SPECIAL TILING BY CONGRUENT CONCAVE Quadrangles
, 2014
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A class of spherical dihedral ftilings
 European Journal of Combinatorics
"... CM{UTAD, Preprint number 1 centro de matematica cm{utad ..."
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CM{UTAD, Preprint number 1 centro de matematica cm{utad
Tilings of the sphere with right triangles III: the asymptotically obtuse families
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Combinatorial tilings of the sphere by pentagons
 Elec. J. of Combi
"... Abstract A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent pentagons. We show that the tiling cannot have only on ..."
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Abstract A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent pentagons. We show that the tiling cannot have only one vertex of degree > 3. Moreover, we construct earth map tilings, which give classifications under the condition that vertices of degree > 3 are at least of distance 4 apart, or under the condition that there are exactly two vertices of degree > 3.