Name for a disk that bisects a ball

Question

In two dimensions, a disk is bisected by lines through its center. These lines are called "diameters". In three dimensions diameters still refer to one dimensional lines through the center of the ball. Is there a widespread term for the bisecting planes (or maybe I should write disks, as they are cropped) of a ball?

Thank you!

Answer 1

It doesn't seem to be an established term, but equatorial disk could be said to carry the authority of William P. Thurston, based on this page from Three-Dimensional Geometry and Topology (1997):

Answer 2

According to the definition given in the Wikipeadi article Bisection, bisection refers to "the division of something into two equal or congruent parts". So given a 3D object like a sphere, if you want to divide it in two parts of equal volume, you do it using a plane. Naturally, such a plane is bisecting the sphere.