[4,4] half-turn (p2)         index 8: TORSION (element of order 2 of parabolic [2, 3] fixes a coset: word [2, 3, 2, 3]) ; orbit-size test: NOT free ; H1=Z/2+Z/4   expected: TORSION
[4,4] torus                  index 8: torsion-free ; orbit-size test: free ; H1=Z^2   expected: torsion-free, H1=Z^2
[5,3,5] Seifert-Weber        index 120: torsion-free ; orbit-size test: free ; H1=Z/5+Z/5+Z/5   expected: torsion-free, H1=(Z/5)^3
[5,3,3,5] Davis              index 14400: torsion-free ; orbit-size test: free ; H1=Z^24   expected: torsion-free, H1=Z^24
[5,3,3,3] sigma=x*s = w0(H4) w0(H3) NOT an action of W (some relation fails)   expected: not an action
[5,3,3,3] sigma=x*w0(H4)     NOT an action of W (some relation fails)   expected: not an action
