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Some New Tilings of the Sphere with Congruent Triangles
Visual Mathematics, Tome 8 (2006) no. 1
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Many years ago, Sommerville classified the tilings of the sphere with congruent spherical triangles ? under some assumptions. Later, Davies did the same, under only the restriction that the triangles should meet edge-to-edge. This paper surveys a recently-discovered class of tilings with congruent spherical triangle tiles that do not meet edge-to-edge.
Classification : 05B45 52C2052C22 
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Robert J. MacG Dawson. Some New Tilings of the Sphere with Congruent Triangles. Visual Mathematics, Tome 8 (2006) no. 1. http://geodesic.mathdoc.fr/item/VM_2006_8_1_a2/