Articles and Tutorials — isoarea

To start folding from crease patterns, we must first decide what part of the pattern to fold - what to put in the center, and how many repeats we want.

Next, we need to actually fold the grid.

Finally, we can start folding!

A Whole Lot of 3   Sometimes it can be hard to tell what's 3 and what's 6. Now this may sound confusing - how can you not know the difference between 3 and 6? But when there's 6 things, with alternation between each one, is it 3 or is it 6? In terms of rotational symmetry, the answer is 3. In terms of twists in a loop, the answer is 6. And to make matters worse, you can't look for 3-fold symmetries around the point in question to decide - they're all going to be 3-fold in either case!...

When we start folding tessellations we're presented with a couple grid options - all of which are aligned with the edge of the paper in some way.

This fact is invisible in the way we talk about grids too.

We don't say "square grid aligned with the edges of the paper" - it's just "a square grid".

If you're already familiar with isoarea tessellations, you might notice something unusual about this one - it uses hexagon twists!

Most of the time you'll see isoarea patterns in tessellations with all the same kind of twist - squares, equilateral triangles, right triangles, and occasionally rhombi.