“3D Thinking” Page 238: Shape Changing Polyhedra
The original idea for shape changing polyhedra came from studying muqarnas and playing with children’s building blocks. The featured image is of the Nasir al-Mulk Mosque Muqarnas in Shiraz, Iran. The building blocks were as in the photo: 
An introduction to the logic of this geometry can be seen in a paper I delivered to the Bridges Conference this August, 2016: http://archive.bridgesmathart.org/2016/bridges2016-225.pdf.
Shape-Changing Polyhedra are three-dimensional forms composed of polygons that are flexibly connected. Of most interest are shape-changing polyhedra ‘shells’ that connect in a modular fashion to fill space – to fill space and still retain their shape-changing characteristics.
Potential applications are endless and include things like packages that expand or contract to fit their contents; super tools that change their shape based on the needed function; robots and solar panels that fold up from a single sheet; shape changing aircraft, see shape transforming furniture, and transforming architectural forms. My work on shape changers is featured in my new book “3D Thinking in Design and Architecture,” to be published by Thames and HudsonApril 2018 and page references are to that book: Amazon USA, Amazon UK, Waterstones UK.
Core 1, Page 240 – Extended Shell 1
Core 1, Page 241 – Extended Shell 1 – Two Combined – Shows “Equilibrium” Positions. Equilibrium Positions are various stable positions / positions of balance for the shape changing polyhedra.
Core 1, Page 301 – Extended Shell 1 – Multiple Combined – Shows Various Equilibrium Positions
Core 2 Page 245 – Extended Shell 2
Core 2, Page 246 – Extended Shell – Multiple Combined
Core 3, Page 248 – Extended Shell 3
Core 12, Page 256 – Shell 12
See MIT origami robot on youtube