Is it possible to change the volume of a closed 3D solid without stretching any of the faces? Folding and bending is allowed.
I think this means that the Gaussian curvature of the faces has to be respected and the connectivity at the edges has to remain, while the volume of the solid changes.
My intuition is that this can't be done. Eg when collapsing a cube through a rhomboid prism to flat, the sides get stretched into rhombi and then a line, so that's no good. Sorry if the question is imprecise at all.
I'm as interested in ways to approach this kind of question as I am in answering it.
Cheers.