“…The above actions give rise to five oriented name group G generators of G action of G on U, V, W B2 Z 2 e e U = −U , e V = V * , e W = W * B3 Z 3 e e U = e 2 3 πi U , e V = W * , e W = W * V B4 Z 4 e e U = iU , e V = W , e W = V * B5 Z 2 × Z 2 e 1 , e 2 e 1 U = −U , e 1 V = V * , e 1 W = W * e 2 U = U * , e 2 V = −V , e 2 W = −W * B6 Z 6 e e U = e 1 3 πi U , e V = W , e W = W V * Table 1: Orientable actions of finite groups on three-torus flat three-manifolds different from the torus. The remaining four nonorientable quotients, originate from the following actions: For full details and classifications of all free actions of finite groups on threetorus see [9,10], note, however, that the resulting quotient manifolds are always one of the above Bieberbach manifolds. It is easy to see that N1 is just the Cartesian product of S 1 with the Klein bottle, whereas N3 and N4 are two distinct Z 2 quotients of B2.…”