Freaky Triangle - Jordan Clarke
I've seen this around quite a bit, and honestly - its the funnest, perhaps silliest thing to do with paper- some glorified form of collage.
Like Jordan Clarke here, mutating children's faces.
I started off with scissors, glue and RUSSH magazine pages -
though recently I've been messing with masking in Illustrator:
images ® 1001 ways
Using faces works best, especially if you keep 1 or 2 key attributes, like the eyes, unmoved.
You need to use a ruler and protractor for precise identical-ness (like equilateral triangles) - otherwise the shapes can't be swapped for one-another seamlessly. Or mix several images together, rescale an aspect of an image and blow it up till it takes up half the page....
hexagons. whiplash curves.