What is the volume of the intersection in the last blog posting? To compute that we decompose the intersection into 7 parts, three caps, and one cube, using PovRay again. That took me another hour.

The top cap can be integrated along its center, and the cube has side length

\(1/\sqrt{2} \)

If I did not a mistake the volume is

\(\dfrac{4}{\sqrt{2}} + 24(\dfrac{2}{3}-\dfrac{5}{6\sqrt{2}}) \)

This is a bit more than 4.