WOLFRAM|DEMONSTRATIONS PROJECT

Three Tilings of the Sphere with Right Triangles

tiling

1

2

3

percentage of tiling shown

72

This Demonstration shows three different tilings of a sphere with right triangles that do not simply fit edge to edge. The triangles used have dihedral angles of

60°

,

°

90

,

75°

(requiring 16 tiles);

60°

,

90°

,

40°

(10 tiles); and

60°

,

90°

,

75°

(72 tiles).