Faceted sculptures and objects are all the rage these days. And they are ideal to make from paper or cardstock.
You don't need fancy 3D-programs or design skills. But it takes time and patience to make them. There's a lot of paper to be printed, cut and glued.
If you want to skip the next steps and just want to build the deer above - Here is the PDF:
It's meant to be printed on A3. You can print it on A4, the deer will then be 75% smaller in the end.
(Please don't share the pdf without the link to where it came from, thank you.)
But you want to make your own, right? So let's get started.
UPDATE: I made a second tutorial for the Moose as some of you have requested.
Step 1: 3D-Model
There are plenty of other models on that site. If none fits you try looking for free .obj or .stl on your favourite search engine.
Most of the time these models were made for animation or 3d-printing. If you were to try to make them detailed like this you'd have to cut out tens or hundreds of thousand little paper triangles. Thats why we have to reduce the level of detail drastically. That way we also get that cool faceted look.
The free software Meshlab (for Windows, Mac or Linux) can do that for us. Get it at: http://meshlab.sourceforge.net/