No cross-caps here. The first puzzle is a torus, the second a Klein bottle. Informally: the Klein bottle has on pair of edges is glued with a twist and one with

No cross-caps here. The first puzzle is a torus, the second a Klein bottle. Informally: the Klein bottle has on pair of edges is glued with a twist and one without; with the cross-cap, both pairs of edges are twisted then glued.