This program is a companion to chapter 4 in the paper,
where I rule out the possibility that the farthest point
set intersects a face adjacent to the antipodal face.

The main idea is that I enumerate all combinatorial types
of pentagon chain corresponding to such a chain.  I then
show that most of these do not correspond to distance
minimizing geodesics.   The remainder have the property
that there is a simultaneous distance increasing variation
for all of them. 

You compile the program using javac *.java
Then you run the program using the command Java Main
