Can the Same Net Fold into Two Shapes?

From Standup Mathematician.

If you cut out the net from the card and solve a fold: send me a photo! Maybe hang it on your tree as a decoration.

To receive a physical card you officially need to be a "statistically significant" supporter (or higher) on Patreon by the end of 06 December 2022. And all supporters get emailed a digital copy!

This is the tweet from Jun Mitani in 2017:
And the recent retweet by Vincent Pantaloni I saw:

Huge thanks to Ryuhei Uehara for did much of this research and was very helpful then I emailed. You can see their page (with all 2263 nets) here:

All the publications I waved around:
2007 – "Geometric Folding Algorithms" by Erik Demaine and Joseph O’Rourke
2008 – "Polygons Folding to Plural Incongruent Orthogonal Boxes" by Ryuhei Uehara
2011 – "Common Developments of Several Different Orthogonal Boxes" by Zachary Abel, Erik Demaine, Martin Demaine, Hiroaki Matsui, Günter Rote and Ryuhei Uehara
2013 – "Common Developments Of Three Incongruent Orthogonal Boxes" by Toshihiro Shirakawa and Ryuhei Uehara
2015 – "Common Developments of Three Incongruent Boxes of Area 30" by Dawei Xu, Takashi Horiyama, Toshihiro Shirakawa, and Ryuhei Uehara

Here is Geometric Folding Algorithms on Amazon if you want your own copy to wave around. But it costs ‘text-book money’.

Huge thanks to my Patreon supporters who funded those crazy nets I was sticking together. Support me and help me make more ridiculous shapes (also: videos).

– At 07:36 I place the top shape in the wrong spot. But it totally works! Look at the diagram!
– Let me know if you spot anything else! My bad taping skills do not count as a mistake.

Filming and editing by Alex Genn-Bash
Props by Lisa Mather
3D plot in Geogebra by Ben Sparks
Written and performed by Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician
US book:
UK book: