Resumen de Spherical simplices and their polars

Kenzi Satô

• This article is about spherical simplices in the unit sphere. One of the purposes is to give a relation of dihedral angles of a spherical simplex and its polar, and the other is to give two simple formulae of volumes of spherical simplices and their polars. We can calculate the volume of a spherical simplex and the sum of volumes of it and its polar from these formulae for the unit sphere in the odd- and even-dimensional Euclidean spaces, respectively.