... 27◦)andvertexvectors(0, 2, 8), (0, 5, 0), (1, 0, 10), (1, 3, 2), (2, 1, 4), and (4, 0, 0). Its area is 1/80 that of the sphere. Theorem 2 The triangle T8does not tile the sphere. Proof: As before, we examine the ... now find the vertex vectors (a, b, c) of the triangles Tn.Proposition 1 The vertex vectors of Tnare precisely (0, 2 ,n), (1, 3, 2), (4, 0, 0); and, ifn is even, (1, 0,3n−42) and (2, 1,n2); ... Tilings of the sphere with right triangles I: The asymptotically right families, Electron. J. Combin. 13 (2006) R48[6] Dawson, R. J. MacG., and Doyle, B., Tilings of the sphere with right triangles...