Tilings of the sphere with right triangles III: the asymptotically obtuse families
نویسندگان
چکیده
Sommerville and Davies classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. However, if the edge-to-edge restriction is relaxed, there are other such triangles; here, we continue the classification of right triangles with this property begun in our earlier papers. We consider six families of triangles classified as “asymptotically obtuse”, and show that they contain two non-edge-toedge tiles, one (with angles of 90, 105 and 45) believed to be previously unknown.
منابع مشابه
Tilings of the Sphere with Right Triangles I: The Asymptotically Right Families
Sommerville [10] and Davies [2] classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. Relaxing this condition yields other triangles, which tile the sphere but have some tiles intersecting in partial edges. This paper determines which right spherical triangles within certain families can tile the sphere.
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عنوان ژورنال:
- Electr. J. Comb.
دوره 14 شماره
صفحات -
تاریخ انتشار 2007