# Articles and Tutorials — math

## Tiling-Based Origami Tessellation Design

Posted by **Madonna Yoder** on

Origami tessellations are infinitely repeating patterns folded from a single sheet of paper.

My designs are in the twist-based style and I fold my patterns one twist at a time whenever possible.

## Siren's Call Origami Tessellation

Posted by **Madonna Yoder** on

There are some patterns that when I see them, I know I have to fold them.

Usually I keep a queue of about 10 of these patterns, but sometimes one skips to the front of the line.

Siren's Call is one of **those**.

## Dancing Pyramids Origami Tessellation

Posted by **Madonna Yoder** on

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!...

## Hybrid Closed Islands Origami Tessellation

Posted by **Madonna Yoder** on

Tiling Surprise Believe it or not, Hybrid Closed Islands has the same tiling structure as Robin Scholz's Celtic Circle. Both of these tessellations feature twists with six pleats (hexagon twists) surrounded by twists with three pleats (triangle twists) and vice versa. However, when you look at Hybrid Closed Islands it's easy to see only triangles - because the six-pleated twists only have three-fold rotational symmetry. Centering Choices In this tessellation, I have three equivalent choices of what to put in the center, and whatever I put in the center will be emphasized in the pattern. Each of these three...

## Rotated Grids Challenge Winner

Posted by **Madonna Yoder** on

## Rotated Grids Challenge

Posted by **Madonna Yoder** on

## Rotating Grids in Squares and Hexagons

Posted by **Madonna Yoder** on