Laser-cutting

Software:

https://inkscape.org/en/
http://www.123dapp.com/make
https://github.com/mkeeter/antimony
http://www.openscad.org/
http://sketchchair.cc/

Origami:

http://www.tsg.ne.jp/TT/software/
http://www.langorigami.com/article/treemaker
http://www.curvedfolding.com/group/freeformorigami

Machine Software

http://fabmodules.org/
https://hci.rwth-aachen.de/visicut
http://inkcut.sourceforge.net/

Inspiration:

http://georgehart.com/sculpture/monsters.html
http://strawbees.com/
https://en.wikipedia.org/wiki/Rubik'sSnake
cardboard-surfboard
http://kartongroup.com.au/
20-creative-cardboard-lamp-ideas/
http://fab.cba.mit.edu/
http://www.thingiverse.com/thing:4764
http://fffff.at/free-universal-construction-kit/
Laser origami
https://de.pinterest.com/karstennebe/press-fit-construction/