Making efficient Platonic and Archimedean shapes in a kaleidoscope

Sign up on Patreon for the SUM xmas card! https://www.patreon.com/standupmaths If you want the physical card you need to be greater than or equal to "Statistically Significant". Physical card deadline: end of 06 December 2022 Digital card deadline: end of 15 December 2022 (In both cases I'll try to accommodate sign-ups after that but no promises). This is why the christmas tree on the card is so low resolution: https://www.youtube.com/watch?v=jOTTZtVPrgo Here is the "Deltoidal kaleidoscopes" paper by Josep Rey Nadal and Manuel Udina Abelló. https://archive.bridgesmathart.org/2022/bridges2022-351.pdf Museu de Matemàtiques de Catalunya aka "Museum of Mathematics of Catalonia" https://mmaca.cat/en/ This is the art show listing from the 2022 Bridges conference in Helsinki. http://gallery.bridgesmathart.org/exhibitions/2020-bridges-conference/josep-rey For both kaleidoscopes make two mirror images of each shape. Deltoidal Hexacontahedron Kaleidoscope Faces: https://www.dropbox.com/s/9tltpyo4v6kjfr6/DeltoidalHexacontahedronKaleidoscopeFaces.pdf?dl=0 Deltoidal Icositetrahedron Kaleidoscope Faces: https://www.dropbox.com/s/jb356rspfn5888c/DeltoidalIcositetrahedronKaleidoscopeFaces.pdf?dl=0 Here is the second channel video from 2017: "How to flat-pack a cube" https://www.youtube.com/watch?v=Kr-yV_T-_9A Huge thanks to my Patreon supporters who funded so many sheets of mirror acrylic. I actually have a bunch left over. Support me and tell me what I should do with the rest of the mirrors. https://www.patreon.com/standupmaths CORRECTIONS - None yet, let me know if you spot anything! My bad taping skills do not count as a mistake. Filming and editing by Alex Genn-Bash Shape calculations by Sam Hartburn Written and performed by Matt Parker 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