Supposing that the sphere $x^2+y^2+z^2=9 $ has four central holes of unit radius drilled through it.
The radial holes are directed towards the sphere center starting from hypothetical regular tetrahedron vertices with included angle $ \cos^{-1} (-1/3) $ between the four directions and stop at the center.
One hole is along the z-axis, one hole has projection along the x-axis in x y plane, other two at 120 and 240 degrees. Find volume remaining after drilling out the four holes.
Motivation is to see if the formidable triple integrals for volume would get simplified using Quaternions along partition planes.