The Euler characteristic for a Coxeter complex based on A_n goes like
chi = (-1)^n.2n.(n - 2)!!(n - 2)!!
which grows quickly but is only -6 for the case of A_3. Goodness me, that number does have a tendency to crop up, doesn't it now?
occasional meanderings in physics' brave new world
Marni D. Sheppeard