Folding 3D surfaces?

We know how to fold 2D object, like in Origami. However, I recently thought about how we would fold 3D surfaces.

Since we fold paper across lines, we might fold 3D surfaces across planes. Is this accurate?

I have attempted to create an illustration of this concept, using the example of a cone folded over a plane situated halfway between the endpoints ($A$ and $B$) and perpendicular to segment $AB$.

• Well, you can fold a three-dimensional figure in four dimensions. But the definition of folding you are using in both cases is different, since a fold in 2D is not a reflection but a rotation. – Anonymous Pi Mar 21 '17 at 18:38
• How is a fold a rotation? I thought that it was to simply reflect across the chosen line. – Drew Christensen Mar 23 '17 at 22:46
• Well, it's a reflection if you fold it all the way. But if you don't, it will be a rotation. – Anonymous Pi Mar 23 '17 at 22:48
• Ah, I see. If only reflects the part being folded. – Drew Christensen Mar 23 '17 at 22:49