It is known that if we identify each pair of antipodal points on the edge of a 2-D disc, we'll have a real projective plane.
Now I'm curious about the structures which are emerged when we identify 3 or more symmetrical points on the edge. (For example for 3 point case we merge each triple points of the circumference which are on 120 degree distant pairwise.)
What can we know about these structures? Are they manifolds?...