Just for fun: here is the square-and-triangle tiling

[Garald]

... or at least the central panel. I have spotted only one error so far. Are there more? (Symmetry should make it easy to spot them.)

 

[ProDave]

Bottom left 2 white triangles, bottom right, 2 blue triangles.  Should be the same.

[Garald]

23 minutes ago, ProDave said:

Bottom left 2 white triangles, bottom right, 2 blue triangles.  Should be the same.

Exactly (though I'd call that color "green", and my more civilized friends call it "teal"). Also, one of the bottom-right white triangles should be teal (again to keep symmetry - both left-right and top-bottom).

[ProDave]

And I thought working out the pattern to tile our floor with 2 different size rectangle tiles and 2 different size square tiles was complicated.

[Garald]

The contractor was remarkably fast (and I'd say he's done a good job). Planning, though, took more days than I'm ready to confess. I chose all the colors by hand - they don't really have a mathematical significance. The triangle-square pattern is in fact significant (https://tilings.math.uni-bielefeld.de/substitution/square-triangle/) and perhaps because of that wasn't so hard for me to do (I hacked up the Python routines to produce Latex/TikZ code within a day).

[Garald]

OK, found another error on the edge.

[saveasteading]

Like a Persian carpet  there should be a flaw, as only God creates perfection. 

 

Good job mortal.

[SteamyTea]

12 hours ago, Garald said:

though I'd call that color "green", and my more civilized friends call it "teal"

Vert verre ver

 

 

[Garald]

Update for the sake of fairness: these turn out to be flaws in the design I sent the contractor last week. I had corrected when preparing a hi-res version with the architect - which she never sent to him in the end, or at least not on time. Since there is no mathematical meaning to the colors, and the errors, being on the edges, don't break the effect of symmetry, I think I'll just let the matter drop. I think it's nice as it is.

 

[SteamyTea]

3 minutes ago, Garald said:

Since there is no mathematical meaning to the colors

https://en.wikipedia.org/wiki/Four_color_theorem

[Garald]

1 hour ago, SteamyTea said:

https://en.wikipedia.org/wiki/Four_color_theorem

Well, sure, I clearly tried to do a three-coloring, but that was going to be strictly speaking impossible due to the D_6 symmetry. And yes, there is a D_6 symmetry which is broken by the imperfections, but that's nothing deep.

[Garald]

At any rate, here there is a version with adjustments to the side panels, respecting the work already made. 

triptych5.pdf

Edited March 4, 2023 by Garald

[SteamyTea]

For your next project, try some pointillism, then maybe work up to chromo-luminarism.

Or just spend a week at Park Güell with a bag of drugs for company. Antoni Gaudí knew a bit about tiling.

As does our @pocster, would set his OCD off bigtime.

[Mr Punter]

The side panels are not mirror symmetrical with the colours.  Is that on purpose?

[Pocster]

1 hour ago, SteamyTea said:

For your next project, try some pointillism, then maybe work up to chromo-luminarism.

Or just spend a week at Park Güell with a bag of drugs for company. Antoni Gaudí knew a bit about tiling.

As does our @pocster, would set his OCD off bigtime.

The cause of ocd is tiling 

[SteamyTea]

12 minutes ago, pocster said:

The cause of ocd is tiling 

The cure is a hammer.

[Garald]

1 hour ago, Mr Punter said:

The side panels are not mirror symmetrical with the colours.  Is that on purpose?

That's on purpose - the central circle (including the central panel but extending onto the sides) has D_6 (dihedral group) symmetry, but outside the circle I can do what I want. I thought it would be interesting to color things very freely outside the circle, emphasizing patterns rather attempting a 3-coloring.

[Garald]

(Another cause of the asymmetry is that I have more teal tiles than white or blue tiles. I ordered more teal tiles simply because I liked the color!)