Article PDF
Avoid common mistakes on your manuscript.
References
Azavedo Breda, A.M.R., A class of tilings of S2, Geom. Dedicata 44 (1992), 241–253.
Coxeter, H.S.M., Regular Polytopes, Dover, New York, 1973.
Davies, H.L., Packings of spherical triangles and tetrahedra, Proc. Colloquium on Convexity, Copenhagen, 1965, pp. 42–51.
Dawson, R.J.M., An isosceles triangle that tiles the sphere in exactly three ways, Discrete Comput. Geom., to appear (DOI: 10.1007/s00454-003-2777-0).
Günbaum, B., and Shepherd, G.C., Tilings and Patterns, Freeman, New York, 1987.
Heesch, H., Eine Betrachtung der 11 homogenen Ebenenteilungen, Mathematikunterricht (1968), 66–78.
Mann, C., An infinite family of prototiles with Heesch number 5, unpublished.
Mann, C., Private communication.
Schwarz, H.A., Zur Theorie der hypergeometrischen Reihe, J. Angew. Math.75 (1873), 292–335.
Sloane, N.J.A., and Plouffe, S., The Encyclopedia of Integer Sequences, Academic Press, San Diego, CA, 1995.
Sommerville, D.M.Y., Division of space by congruent triangles and tetrahedra, Proc. Roy. Soc. Edinburgh 43 (1923), 85–116.
Ueno, Y., and Agaoka, Y., Classification of the Tilings of the 2-Dimensional Sphere by Congruent Triangles, Technical Report 85, Division of Mathematical and Information Sciences, Hiroshima University, 2001.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dawson , R. Tilings of the Sphere with Isosceles Triangles. Discrete Comput Geom 30, 467–487 (2003). https://doi.org/10.1007/s00454-003-2846-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00454-003-2846-4