The shape that should be impossible.

Stand-up Maths

Get your Sydler-shape limited-edition dust jacket now! https://mathsgear.co.uk/products/love-triangle-by-matt-parker-signed Here is the bonus video with all the details: https://youtu.be/cB18rgH5YaM 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-triangle/matt-parker/9780241505694 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/sydler-pi4-polyhedron-final-70cf6dda7f6545dcb827bcec87fb526b Henry Segerman's video: https://www.youtube.com/watch?v=tH6vLXMaCwQ&ab_channel=HenrySegerman Robin's 15° shape: https://sketchfab.com/3d-models/single-angle-15-coloured-8230e145f97c4daba4cfbaf317f0a55b 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. https://www.patreon.com/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/books/610964/humble-pi-by-matt-parker/ UK book: https://mathsgear.co.uk/collections/books/products/humble-pi-signed-paperback