Elliptic geometry geometry is that the sum of the interior angles of a triangle is greater than 180 degrees. In the spherical model, for example, a triangle can be constructed with vertices at the locations where the three positive Cartesian coordinate axes intersect the sphere, and all three of its internal angles are 90 degrees, summing to 270 degrees. For sufficiently small triangles, the excess over 180 degrees can be made arbitrarily small. The Pythagorean theorem fails in elliptic geometry. In the 90°–90°–90° triangle described above, all three sides have the same length, and consequently do not satisfy formula_1. The Pythagorean result
Moser spindle graph" has also been applied to a different graph, in the form of a triangle inscribed within a hexagon. As a unit distance graph, the Moser spindle is formed by two rhombi with 60 and 120 degree angles, so that the sides and short diagonals of the rhombi form equilateral triangles. The two rhombi are placed in the plane, sharing one of their acute-angled vertices, in such a way that the remaining two acute-angled vertices are a unit distance apart from each other. The eleven edges of the graph are the eight rhombus sides, the two short diagonals of the