Making efficient Platonic and Archimedean shapes in a kaleidoscope

From Standup Mathematician.

Sign up on Patreon for the SUM xmas card! 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:

Here is the "Deltoidal kaleidoscopes" paper by Josep Rey Nadal and Manuel Udina Abelló.

Museu de Matemàtiques de Catalunya aka "Museum of Mathematics of Catalonia"

This is the art show listing from the 2022 Bridges conference in Helsinki.

For both kaleidoscopes make two mirror images of each shape.
Deltoidal Hexacontahedron Kaleidoscope Faces:
Deltoidal Icositetrahedron Kaleidoscope Faces:

Here is the second channel video from 2017: "How to flat-pack a cube"

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.

– 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
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UK book: