The following is meant to be a depiction of quotienting a square by each of its sides, with a grid inside. I want to preserve the intersection points in the grid. I first quotient each side of the square. Then, I identify the black point with the green point, and the pink point with the yellow point.
Let $X$ be the original square. Then I was able to write down $X/ \sim = \{ [x] : x \in X \},$ where $[x]$ is the equivalence class of $x.$ I'm stuck at this point.
What is the final topological shape homeomorphic to?
