Starting from an intersection of the vertices of a tetrahedron with a sphere;
Is it possible to recursively divide the 4 spherical triangles into 4*4 = 16 smaller triangles according to the pattern below?:
Is self-similarity preserved when dividing the spherical triangle into 4 equal spherical triangles? In other words, can you keep dividing the spherical triangles ad infinitum?
[EDIT:] Due to spherical Excess the angles of the smaller spherical triangle will be different than the larger spherical triangle. If a spherical triangle is defined by angles a,b,c, alpha, beta, gamma is it possible to find equations to determine these angles using the number of divisions? Inother words the number of times a large spherical triangle has been partitioned in 4 spherical triangles?