The eight regions of space defined by the eight possible combinations of signs for $(+/- , +/-, +/-)$ for $x$, $y$, $z$ are called octants.
Given a ball of radius 1 centered in the origin $(0, 0, 0)$. How are the eight sections called obtained by the intersection of the ball with the octants?
More generally, given a (regular) triangulation of the sphere (I hope such a thing exists). Now connecting such a spherical triangle with the origin how are the pieces cut out of the (unit) ball this way called?
Pointer to literature on these topics are appreciated.