Wonky Quadrilaterals


Last summer I got caught up with a shape that Martin Holtham started looking at after seeing this vase in a furniture store.

from this fun twitter thread https://twitter.com/GHSMaths/status/757688653795758080
from this fun twitter thread https://twitter.com/GHSMaths/status/757688653795758080

Martin made some paper models of the vase, and I tried it out, too, then explored other ways of decorating, folding and cutting this shape.

Quadrilaterals, decorated
Quadrilaterals, decorated

With Martin’s help I made this template for folding:

I kept getting stuck . I liked much of what was happening but was never quite satisfied with what I came up with.

Recently I decided to revisit this shape again. I questioned the materials I was using,  decided to work in a 11″ x 17″ format, started looking more at what the shapes wanted to do than trying to impose my own thoughts on to them.

What’s notable about this shape is that it has an irregularity to it that does not let it fill up a piece of paper in a typically symmetrical way.  It moves somewhat diagonally across the surface. So I went with that and came up with a different template.

Wonky Quadrilateral net
Wonky Quadrilateral net


Going along with the flow of the shape made all the difference!


It folded down into adorable little structure that does a twist-fold , collapsing all the quadrilaterals into this unruly many-sided shape…

 …which untwists in a truly lovely way.


I’m still working on this. There are still some thing that I need to work out, not the least of which is to figure out how to make a little video of this structure expanding and contracting again. I have to do it in the right light with a tripod, and I haven’t been able to get it right.

Even though this is still a thought-in-progress, I am so enamored with how it’s progressing that I wanted to share it now.

Idea in motion
Idea in motion

2 thoughts on “Wonky Quadrilaterals

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