Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 2, pp. 447461 (2004) 

Dihedral ftilings of the sphere by spherical triangles and equiangular wellcentered quadranglesAna M. d'Azevedo Breda and Altino F. SantosDepartment of Mathematics, University of Aveiro, 3810  193 Aveiro, Portugal, email: ambreda@mat.ua.pt; Department of Mathematics, U.T.A.D., 5001  911 Vila Real, Portugal, email: afolgado@utad.ptAbstract: The classification of ftilings was inspired in Stewart Robertson's work [R], ``Isometric Foldings of Riemannian Manifolds'' and was initiated by Ana Breda [B], where a complete classification of all monohedral ftilings of the Riemannian sphere $S^{2}$ was done. Here we shall classify, up to a spherical isometry, the class of all dihedral ftilings of $S^{2}$ whose prototiles are spherical triangles and well centered spherical quadrangles with all congruent internal angles. Table 1 and Figure 19 give a summary of the families involved in this classification. [R] Robertson, Stewart: Isometric Folding of Riemannian Manifolds. Proc. Royal Soc. Edinburgh {\bf 79} (1977), 275284. [B] d'Azevedo Breda, Ana M.: A Class of Tilings of $S^{2$}. Geometriae Dedicata {\bf 44} (1992), 241253. Keywords: WCSQ, dihedral tilings, isometric foldings, spherical trigonometry Full text of the article:
Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.
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