There are some based on rectangles (click a model's images to go to its 3D Warehouse page):
Babies and Monsters (the babies are upside-down)
One tessellation is based on a triangle:
And my favorite is based on a hexagon:
Here's what Garret had to say, on how he came up with these patterns:
I just started with a shape (a square, rectangle, triangle, etc.), and simply drew a few lines here and there on each side, copying them to the appropriate opposite side. After that, I just tried to see what kind of artistic figure I could make out of the shape that I had created. On a few, I adjusted the entire tile to fit more closely to some figure that the tile resembled. Otherwise, it was just random.
I posted a project on the Math Forum last year on how to make rectangular Escher patterns. Go here, and scroll down to October 2009. Triangular and Hexagonal patterns are similar; both involve copying lines and arcs from one polygon edge to others.
Anyone can design anything in 3D! http://www.3dvinci.net/