So one of the youtubers I watch is Mathologer aka ‘Burkard Polster’ who makes interesting and very clear videos about recreational Mathematics. One of the recent ones I watched was on ‘Heron’s formula’ which was about area and perimeter calculations.
In any case, one of the examples used was a right-angle triangle with sides (3, 4, 5) and an inner circle (?) - ok, no the ‘incircle’ - has a radius of 1. Interesting by itself (go watch the episode! ). Also, though, I reckoned I could tile these triangles and get an interesting pattern.
So it turns out that it looks like a sort of skewed square/octagon tiling. I made it slightly different with some curves, but that’s the basic idea:
The symmetry is a bit weird. I tried to 3-colour it, which should be possible, but I messed it up a bit when designing it on a skeleton of the tiling. Ho-hum.
A different version of the same thing is on Etsy.