Are Circles Triangles and Squares topologically homeomorphic?

Question

I'm trying to get the fundamental group of a square figured shape having four triangular subdivisions by its two diagonals using Van Kampen's Theorem. But The first question that came to my mind is that, Is a triangle and a circle homeomorphic? And If yes, then I can imagine it to be homeomorphic to a square too. But A square can be turned into a Torus. and Torus and Circle are not homeomorphic. Where I'm making mistakes?