An elementary proof of sforza-santaló relation for spherical and hyperbolic polyhedra

We defined and studied a naturally extended hyperbolic space (see [1] and [2]). In this study, we describe Sforza's formula [7] and San- taló's formula [6], which were rediscovered and later discussed by many mathematicians (Milnor [4], Suárez-Peiró [8], J. Murakami and Ushijima [5], and Mednykh [3]) in the spherical space in an elementary way. There- after, using the extended hyperbolic space, we apply the same method to prove their results in the hyperbolic space.