Guards in polyhedra solution

Duncan (
Sat, 14 Sep 1996 12:56:20 -0700

Hi everyone,
Who has the solution to Guards in polyhedra (question 6, p.12,
Computational Geometry in C, by Joseph O'Rourke --- the book we used at
Princeton?) Let me copy the question for you:

Design a polyhedron such that guards placed at every vertex fail
to cover completely the interior. A polyhedron is a three-dimensional
version of a polygon, composed of polygonal faces, and enclosing a

I assigned this problem as a part of the Art Gallery project for
my students last week and realized that I don't have a solution for that.
I tried to find a solution with toothpicks and marshmallows the last two
days and found myself back to square one.

If you have a solution please fax it to

Duncan Chiu, 201-833-5403

Thanks. duncan