Unless anyone objects today, I will notify Soifer accordingly.

]]>Something we must not forget in the paper: I just realised that the slanted edge 9-10 in Jaan’s picture is not precisely parallel to the edge 2-3 – the slopes are about 2.4996 and 2.4217 respectively (this is for the standard 6992 case). This means that there needs to be a zigzag in the middle of the 9-10 edge, so that the central section is exactly parallel to 2-3. So our large tiles get four extra vertices.

]]>I guess now is the time to switch our attention to five colours. I’m simultaneously pursuing several other strands of the paper, as you can see, but I’ll try to do something.

]]>Ten out of ten digits match. It’s a miracle.

]]>Ah, damn, I maligned you! I was the one with the bug – I was indeed calculating the number using w=1/2. I now obtain 6043.112468 with (0,0.0143908), (0.000721488,0.0115263), (0.00400433,0.00385627), (0.00630569,0), (0.970075,1/4+a/2), (0.863862,1/2+a).

]]>Hm, I’m not having any such problems with reproducibility. Also, I’m checking the lengths of diagonals arising from the returned values and they are all coming out exactly right (well, to within 10^-15). I think you must have a bug somewhere.

]]>Looks good! Meanwhile I have figured out an elegant way to encode skewing, so I will try a few more things today. I will also export the clause lists for these graphs so that those with superior SAT solvers can attack CN=8 for the various spheres.

]]>Actually there were several more (including two neighbouring red hexagons that are visible on your screenshot). I hope I have corrected the colouring now:

https://drive.google.com/drive/folders/1YsP8wd5h8pFkfjLsd6eOZuGdTJ-SA3-m?usp=sharing

]]>Thanks, Aubrey. I am not surprised. Whenever I run optimization, I get a new result. It is like a random number generator. Our results may coincide accidentally, but we will never know the right one.

I substituted your values and got 6042.52977236409. But some distances are slightly more than 1. I also got almost your 5874.63162557873, if instead of w, I use 0.5 when calculating the total area.

I’ll try to get Mathematica to render some 9-colourings soon.

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