This is similar to the more popular origami research:

Origami Transformers: Folding Orthogonal Structures from Universal Hinge Patterns:

http://erikdemaine.org/theses/aovadya.pdf

Geometric Mechanics of Curved Crease Origami:

http://arxiv.org/abs/1206.0461

Notes on Some Geometric and Algebraic Problems Solved by Ori gami:

http://arxiv.org/pdf/1409.4799v1.pdf

Everything Demaine speaks about is original (at least to me). Even his data structure class is about rarely talked about like succint, persistent ones.