Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 2, pp. 447-461 (2004)

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Dihedral f-tilings of the sphere by spherical triangles and equiangular well-centered quadrangles

Ana M. d'Azevedo Breda and Altino F. Santos

Department of Mathematics, University of Aveiro, 3810 - 193 Aveiro, Portugal, e-mail:; Department of Mathematics, U.T.A.D., 5001 - 911 Vila Real, Portugal, e-mail:

Abstract: The classification of f-tilings 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 f-tilings of the Riemannian sphere $S^{2}$ was done. Here we shall classify, up to a spherical isometry, the class of all dihedral f-tilings 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), 275--284.

[B] d'Azevedo Breda, Ana M.: A Class of Tilings of $S^{2$}. Geometriae Dedicata {\bf 44} (1992), 241--253.

Keywords: WCSQ, dihedral tilings, isometric foldings, spherical trigonometry

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Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.

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