Geodesic
Tilings of the sphere with right triangles. III: The asymptotically obtuse families
The electronic journal of combinatorics, Tome 14 (2007)
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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-to-edge tiles, one (with angles of $90^\circ$, $105^\circ$ and $45^\circ)$ believed to be previously unknown.
DOI : 10.37236/966
Classification : 05B45 
@article{10_37236_966,
     author = {Robert J. MacG. Dawson and Blair Doyle},
     title = {Tilings of the sphere with right triangles. {III:} {The} asymptotically obtuse families},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/966},
     zbl = {1157.05021},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/966/}
}
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Robert J. MacG. Dawson; Blair Doyle. Tilings of the sphere with right triangles. III: The asymptotically obtuse families. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/966

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