Flexagons are structures created by folding strips of paper, that can be flexed or folded in certain ways to reveal more faces than were originally on the back and front.
Here's an example of a cross flexagon book from Crossett's collection of artists' books. Ask the library staff if you'd like to view it.
Paper engineer David A. Carter has a website with PDFs of templates for many of the pop-ups featured in his book The Elements of the Pop-Up which the library owns.
Accordion folds are simple but need to be done precisely. They are a versatile and useful technique.
Accordion folds are used in creating hinge spines, flag book binding, and tunnel books. The pages of a tunnel book are bound with two folded accordion strips on each side so when viewed through a hole in the cover there is an illusion of depth and perspective.
Here's an example of a tunnel book in action —The Tunnel Calamity by Edward Gorey