SLawton has discovered Pepakura, Paperkraftieren etc
"Mixed Media Pepakura Paperkraft".
you can 'sandwich' the paper, cardboard, foamcore, APEC-5/7 transparent OHT architectural decal,
to make "Pepakura Lanterns" etc, which can be light-up with those "LED tea-lights"
like Fran of FranLab discusses.
It's all good. The borg are lucky -
most of our geometries already exist as nets to be printed and folded. Tetrahedra, etc.
The Electronic Journal of Combinatorics has over 2.5 million nets, for example.
there are then other locales, papercraft directories etc.
you can then extrapolate to CNC'd or Lazer-etch very quickly from the paper-mock-up.
For those compound-curves (like a Ricci-Perelman "undulating 3Sphere" etc)
you need to look into dedicated Origami techniques and rollers etc.
That's when you'll discover Yutaka "Boomerang Prof" Nishiyama etc or, Kai Huang-Yueh's and Yiu WuXhei's origami.
you can fold a dome out of APEC7 packaging "upcycling" recycling,
and that is quicker than the printer for most stuff hehe.
1 - measure twice, cut once. Use a decent protractor or 'plumb-bob' and pin jig set,
such as a cork-board, for marking out your folds.
2 - "fold of material", it's always a little more, so, allow a 'lee-way' around the edges of ~0.5-1.5mm (this changes between materials and Material-Material junctions, such as "Hopf-Fibration Pepakura", or "Conway-Coxeter-Schlafli" pepakura).
3 - Scotchguarding or using materials that are water-resistant.
You'll need either the wax-satin-finish or to coat your result in something like UltraEverDry (paper-ligininase variant).
otherwise, take a photo of your creation as it will melt in a humid environment.
4 - "Slot-n-Tab"/ "Biscuit Dovetail Joint" - you need to think of tab-placement and how that will impact on the lighting of your lantern.
Weight -you must use trusses or corfluting for structures which exceed the weight above,
so, most projects won't be like a "flying kite", therefore, you can use card etc. but, this is important for back-of-mind.
So, there's 180GSM SemiSatin "Foamcore" Available at your craft store;
that will do most stuff.
you can use Lazer-CNC'd 280 GSM for the 'structural' frame, or MDF at that point if thickness exceeds ~25mm.
I use Microsoft Visio (with Powerpoint pluggin) and Paint for most of my pepakura,
as well as a GIMP-pluggin for Origami.
I then print that out,
adhese that to the material/s, put that on the 3DPrinter (Repetier K8203b with Lazer-cutter CNC attachement...)
and bingo-bango-bongo, that cuts my Pepakura neater than I could!
I hope this helps -
I am not a pro at all,
though another fan of Pepakura/Paperkraftieren etc.
My better-half is an origami queen, she's very good at helping with the pinch-pletes and Flexagonal stuff.
so, don't be afraid to outsource to your local Artists Swap-Cards club/ Scrapbooking Society for projects