The construction proposed by David Harden is *extremely* similar to the construction of the E8 lattice from the icosahedron, explained in Conway and Sloane’s book.

You will likely find Section III. CONSTRUCTING E8 FROM THE H4 600-CELL interesting, since it has references and discussion related to this post (and cites your paper, along with Dechant’s on the same topic):

[4] P.-P. Dechant, Proceedings of the Royal Society of London Series A 472, 20150504 (2016), 1602.05985.

[5] J. C. Baez, ArXiv e-prints (2017), 1712.06436.

Good for raising young Pythagoreans!

]]>Will do! I was in Copenhagen for a ‘Workshop on Mathematical Trends in Reaction Network Theory’ in the summer of 2015, and I blogged about it here. I enjoyed that town a lot, but I have no idea when I’ll be there again.

]]>For a reference on association schemes that is available for free online, Chris Godsil has a set of notes on them that you can find here: http://www.math.uwaterloo.ca/~cgodsil/mine/notes.html

]]>Unfortunately I won’t be there. I left CQT in 2015, and now I am at the Technical University of Denmark. I don’t currently have any plans to be in Singapore this summer, but I’ll let you know if my plans change. Let me know if you ever come to Copenhagen!

]]>By the way, David: any chance you’ll be at the CQT this summer? I may be there. Maybe we could talk a bit more than last time.

]]>WOW! You solved a bunch of puzzles!

I still don’t know the answers to puzzles 1 and 2. I knew the answers to puzzles 3, 5 and 6, though I only knew the answer to puzzle 6 due to a footnote in Coxeter’s *Regular Polytopes* which doesn’t contain any proof, just a statement of the answer, so it’s reassuring to have some confirmation. I didn’t know the answer to puzzle 4; now I do! So there are 280 ways to partition the 120 vertices of the 600-cell into the vertices of 15 orthoplexes! Great.

I don’t mind someone using a computer for these. *Getting the answer at all* is hard enough. It’s often easier to come up with a human-readable proof after you already know the answer.

Merry Christmas! It’ll take me a while to really digest what you wrote, since I’ve never heard of ‘association schemes’, but I wanted to reply right away.

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