A list of all surfaces (with or without boundary, orientable or nonorientible etc…) classified according to Euler characteristic, orientibility etc.

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Do you know any book, website or any kind of source where I can find the whole list of surfaces classified according to the Euler characteristics. Well, the whole list can’t exists in this universe since it would be an infinite list. But I want to see for example all surfaces (with/out boundary, non/orientable etc.) having Euler characteristic $0$ upto homeomorphism.