Duncan Birmingham
A Guide to Pop-Up

Most pop-up models are built around a basic shape.
 

The shapes are constructed using variations and combinations of pop-up’s two major “building blocks” - the V-Fold and the Parallel Fold.

The same three rules apply to both types of mechanism:-

Every pop-up must span a gully. 
The first gully is the spine fold down the middle of the base card.

Pop-ups must be “balanced” - or match - on each side of the gully. 
With V-Folds the angles on each side must balance. (A + B = A + B)
With Parallel Folds the lengths must balance. (A + B = A + B)

Every pop-up creates new gullies
Additional pop-ups can be built onto these new gullies.

V-Fold
The three creases on the pop-up piece all converge at the same point on the spine.

Parallelogram
The three creases on the pop-up piece are all parallel to the spine.

 

This is the basic theory in a nutshell. Both types of shape have numerous variations. All of which can be modified and combined to produce the complex pop-up structures found in books and cards. A comprehensive exploration of the shapes, and how to build them, is contained in my new book “Pop-Up Design and Paper Mechanics”.