I saw your question, it seems like a game. I am not a mathematician, just a physician, but I would like to post my answer anyways. A solid sphere (not a hollow one because that would have an inside and an outside) has only an outside.

(Sorry is this is too simplistic, but it seemed okay to me and it wasn't mentioned in you list above.)

Dear Gary,

Thanks for your kindly answer.

But any surface can be one-sided (non-orientable) or 2-sided (orientable).

I have to say that It should be not solid.

Best, Erhan

Dear Erhan Güler ,

I'm not sure about Fig. 18 b:

https://www.mdpi.com/2227-7390/7/2/125/htm

Best regards, Joerg

Dear Joerg Fricke,

It is exactly one sided.

" ... Another approach to generate a non-orientable surface starts with a single circular disk from whichtwo tubular stubs emerge in opposite directions (Figure 18a); this is known as Dyck’s surface [67].If these two stubs are joined together with a toroidal loop, one obtains a single-sided 2-manifold (Figure 18b). ... "

Thanks for your information.

Best, Erhan

see also

https://mathcurve.com/surfaces.gb/dyck/dyck.shtml

I think you look for sum of projective planes minus arbitrary set of isolated points, those are all the non-orientable surfaces at first glance.

Dear Roberto Giménez Conejero,

I look for one sided (not solid) surface other than Möbius, Klein, Henneberg, Meeks, Roman (Steiner's), Boy, cross cap, real projective plane !

Best, Erhan Güler

Erhan Güler , what do you mean by "surface"? Is it a 2-manifold? If yes, consider the following construction. For any integer k let P_k be a copy of a projective plane. Then "glue" together (i.e. perform a operation of connected sum) P_k with P_(k-1) and P_(k+1) for every k. You will get a nonorientable 2-manifold (not compact).

A connected sum of any of those, possibly punctured.