There are two different simple versions of spheres with holes.

Sphere with up to 6 coordinate planes parallel holes

In order to arrange the holes freely, a different procedure is required.

A version uses a division of the hemispheres.

http://threejs.hofk.de/sphere/SphereCutAsWanted.html

The position and size of the circular holes is limited.

**The triangulation according to an algorithm by E. Hartmann is much more flexible.**

See

Chapter 7

TRIANGULATION OF IMPLICIT SURFACES

I adapted / simplified the algorithm for the simple case of the sphere and also used an alternative angle calculation.

http://threejs.hofk.de/Triangulation/TriangulationSphereWithHoles.html

The structure of the procedure:

How to add a hole:

Hole defined by points: