Rotated Grids Challenge

Here is my challenge to you: fold a tessellation on an appropriately rotated grid and post a photo before May 12th for a chance to win a unique mini suncatcher, folded and framed by me!

I discovered the value of rotated grids very recently, and now I’m trying to share this simple technique to create cleaner, better-looking tessellations with as many people as possible.

The Rules

• The grid must be rotated so that the grid lines are not parallel to the edges of the paper

• The rotation must align repeating elements of the tessellation with at least one edge of the paper

  • Note that for tessellations with certain symmetry elements, alignment with all edges of a regular polygon is not possible

• The tessellation must be made recently, at least since I published the rotated grids math on April 5th

To Enter

• Post a photo to Facebook or Instagram and tag me (@gatheringfolds) in the photo or description before May 12th
• The photo can be posted to your Feed or Stories, and you’ll know I’ve seen it when I share it in my Stories
• I also plan to share collages of submissions to my main feed - let me know if you want to opt out of me sharing your photos
• I will share as many tessellations as you submit, but there is only one entry to the contest per folder

The Prize

• The winner will be randomly selected from all entrants
• I will send this Lens Stars mini suncatcher (folded on a rotated grid, of course) to the winner

Useful Resources

You can read all about how to calculate the references for your rotated grids on my previous blog post.

The brief refresher is that for square grids on squares, the references are at $// <![CDATA[ \frac{a}{L}=\frac{1}{2}(1-\frac{y}{x}) // ]]>$ , where $// <![CDATA[ \frac{a}{L} // ]]>$ is the fraction of the edge up from the bottom right corner, and $// <![CDATA[ x // ]]>$ and $// <![CDATA[ y // ]]>$ describe the horizontal and vertical changes along a line between two repeating elements in a crease pattern, respectively. Recall that $// <![CDATA[ y // ]]>$ is negative for negative slopes in this line, and positive for positive slopes.

For triangle grids on hexagons, the references are at $// <![CDATA[ \frac{a}{L}=\frac{y}{x+y} // ]]>$ , where $// <![CDATA[ \frac{a}{L} // ]]>$ is the fraction of the edge up from the bottom right corner, and $// <![CDATA[ x // ]]>$ and $// <![CDATA[ y // ]]>$ represent distances along grid lines with $// <![CDATA[ 120^\circ // ]]>$ between them, such that these distances describe a triangle with the endpoints of the third edge at repeating elements in a crease pattern.

The edge markings are rotationally symmetric around your paper - simply rotate the next edge into position and fold the same fraction again. I typically use a second sheet with a reference grid to mark these fractions - no need for additional marks.