Puzzle: Start with a vertically flattish spheroidal surface, and make one Y-shaped cut in the top surface and an identical Y-shaped cut in the bottom surface. Each leg of each Y, after being cut, gives rise to two edges that we'll call "neighbors". Now identify each of the 12 edges created this way with one other of these 12 edges, as follows: Given an edge on top, identify it with the neighbor of its corresponding edge on the bottom. The resulting depiction of a surface in 3-space can be thought of as crossing itself along three segments sharing a common endpoint, making a Y in space: * * * | * | * | / \ * / \ * / \ * * * * * QUESTION: Identify which topological surface this depicts among all the compact connected surfaces without boundary.* --Dan _____________________________________ n * Which are the sphere S^2, the connected sum of n tori # T^2 for any n >= 1, k=1, n and the connected sum of n projective planes # P^2 for any n >= 1. k=1