[net.math] So you think you're good at geometry?

kragness@stolaf.UUCP (Jeffrey G. Kragness) (01/13/84)

We are working on a sphere-packing problem and are trying to find
the volume of the gaps formed when spheres are packed together
in their optimal way.  We are running up against a wall and
if anyone could offer some suggestions as to how to solve the following
sub-problem, it would help us a great deal:

What is the volume of the intersection of a sphere of radius
one and a regular tetrahedron with a vertex at the center of the sphere?
(The tetrahedron can be considered to be very large.)