A tetrahedron inside a sphere can divide a sphere into 4 equal spherical triangles.
What are the angles, coordinates of vertices and arc lengths of those spherical triangles?
Bear in mind link:
Since the sides of a spherical triangle are arcs, they can be described as angles, and so we have two kinds of angles:
- The angles at the vertices of the triangle, formed by the great circles intersecting at the vertices and denoted by Greek letters.
- The sides of the triangle, measured by the angle formed by the lines connecting the vertices to the center of the sphere and denoted by lower-case Roman letters.