@DaniLaura
I really like your Cairo Turtle design!
I just tried 3D printing a version and it looks awesome!
The irregular pentagons of a Cairo tiling may be more visible here, changing angles and eventually degenerating to 4-sided figures.
This has resulted in my art gallery submission for JMM 2025.
https://gallery.bridgesmathart.org/exhibitions/2025-jmm-art-exhibition/rashmi-sunder-raj
Some #CairoTiling-like things that I made of regular edge-touching 12-gons (#dodecagons) a couple of years ago.
The first picture is called “ A Snub Can Lead to a Dual” (http://gallery.bridgesmathart.org/exhibitions/2022-joint-mathematics-meetings/rashmis)
Edit: oops I forgot the alt text on the second picture. It is just an approximation of a part of a Cairo tiling like the first picture, but the dodecagons in each irregular pentagon are more densely packed and are coloured in shades of grey. The effect is more curvy.
Here is another one of the #CairoTiling clips from a couple of years ago. In this one, the rotating and size-changing squares which create the pattern should be somewhat visible.
You might find this picture somewhat interesting, I call it “Cairo Transitions”, and it is from about 4 years ago.
It shows a square grid being transformed into a #CairoTiling by emphasizing different edges in a 3D “bent #pentagon” tiling.
The underlying pattern was created based on the fact that #cubes fit nicely into #dodecahedrons (as mentioned by @johncarlosbaez in this recent post https://mathstodon.xyz/@johncarlosbaez/109290809194904775).
There is a chance that you might have seen it at JMM2020.
massimiliano
Dani Laura (they/she/he)
R. Sunder-Raj
Alexandre B A Villares 🐍