Papers and web sites
| For regular figures in the hyperbolic plane a
simple calculation shows that we can have a tiling (p, q) provided that
1/p +1/q < 1/2 (*)
In fact we can show that for an angle 2Pi/q successive reflections can never overlap and the regular figure tessellates the plane with q meeting at a point. In the hyperbolic plane we have regular triangles with angles from 0 up to but not including 60, the Euclidean case. By (*) above the smallest q we can have is 7, giving an angle of 51.4 degrees. There also exist (3,q) tilings for q = 8 (45 degrees) q = 9 (40 degrees) so on for all q >7. Adjust the point M to close the gaps for the (3, 8) and the (3,
7) tilings.
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Trebly asymptotic trianglesPapers and web sites
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