I’m sorry, but at some point I got out of it mentally. I obviously don’t have the patience of @PavelBoytchev, whom I admire for this in many answer series.
The InnerGeometry Inner Geometry (Triangulation) is the most complex variant and I can’t understand why you need it.
One basis of this is Triangulation sphere with holes
( => TriangulationSphereWithHoles)
You want to do something with a sphere, don’t you 
I have specified the parameters on Github. see e.g.
GitHub - hofk/THREEi.js: three.js addon for triangulation of implicit surfaces and for forms with holes. The addon generates indexed BufferGeometries.
Good luck with this.