The shape that should be impossible.

Get your Sydler-shape limited-edition dust jacket now! https://mathsgear.co.uk/products/love...
Here is the bonus video with all the details:    • Making a dust jacket from an art prin...  

See some of you at the Copenhagen Developers Festival, 28 August 2024
https://cphdevfest.com/

Thanks so much to Paul Catherall who made these beautiful prints. https://www.paulcatherall.com

If you order Love Triangle on Waterstones you will not get the dust jacket but you can use the use the discount code 1+2+3+4+5+6=21 to get 21 percent off the already discounted price. https://www.waterstones.com/book/love...

All UK options: https://www.penguin.co.uk/books/44315...
All USA options: https://bit.ly/3wCTesR

Matthias Goerner's page about Sydler's shape: https://www.unhyperbolic.org/sydler.html

Or see the 3D model directly here: https://sketchfab.com/3d-models/sydle...

Henry Segerman's video:    • The pi/4 polyhedron  

Robin's 15° shape: https://sketchfab.com/3d-models/singl...

CONJECTURE DISCLAIMER:
We believe that the "there must exist a single-angle polyhedron for any angle θ with an algebraic sine" conjecture is true but don't have a nice proof. There seem to be all the required parts for the proof in papers by Sydler and Jessen, but it's not fully assembled.

Huge thanks to my Patreon supporters. They keep me orthogonal.   / standupmaths  

CORRECTIONS
- None yet, let me know if you spot anything!

Filming and editing by Alex Genn-Bash
Written and performed by Matt Parker
Produced by Nicole Jacobus
Music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
US book: https://www.penguinrandomhouse.com/bo...
UK book: https://mathsgear.co.uk/collections/b...