Does the sphere S2 admit a regular tiling with 8 triangles W
Does the sphere S^2 admit a regular tiling with 8 triangles? With 9 triangles?
Solution
The triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane. Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degrees.
With 8 triangles with internal angles 45o whish will give rise to an asosceles right angled triangle which occupy the full angle and triangonal tilling is possible.
With 9 triangles it is not possible with the same reason,
