Scientists came up with concepts that describe the properties of folded objects. I will attempt to explain them here. It is mostly explanation by example.
Take a piece of cardboard with at least one straight edge and divide it in two corners.
Rotate them around a point and use them as a template to draw four lines.
Make mountain folds from three lines. Make one valley fold. Collapse the paper and try to lay it flat on the table. If it dos not work swap the valley fold with one of the mountain folds. This is called “Kawasaki’s theorem.” You can find a further explanation in a Wikipedia page. here
Do it again with the cardboard divide it in three corners. Use four mountain folds and two valley folds.
The miura ori fold is an example of linkage.If you pull or push the right and left side of the paper, the other directions will also respond by folding or unfolding.The word comes from mechanical linkage.
A folded object is rigid when it can be folded and unfolded without deformation.