This is an idea I had for a square grid tessellation. I don't fiddle around too much with square grids. Hexagons just intrigue me more. They're more mysterious.
But I thought this was a pretty neat design.
It's 4x4 squares collapsed on the grid. So you just have a grid filled with 4 pleat squares. No gaps.
I used a 32 pleat grid.
Then you can spread and squash the corners into 3D tirangular shapes.
You can get different patterns based on which corners you squash and in which direction you fold the squashes.
I used standard printer paper. Spread squashes are not easy on pulpy paper. Different paper may produce more consistent results.