# How can I judge a torus and picture's surface is homeomophic or not?

I think that image's surface is like Möbius. So not homeomorphic to sphere. How can I judge and explain about that in usual topology $$\mathbb{R}^3$$?

• Looks like an orientable surface of genus $2$ to me. – Angina Seng Oct 11 '19 at 0:37
• It's important not to get confused with how a surface is embedded iin R^3 and its homeomorphism type. – Andres Mejia Oct 11 '19 at 4:09