–3/2 is the dot product between two nearest neighbours among the set of points on the hyperboloid whose 2×2 matrices have Eisenstein integer entries.
So this is consistent with your guess that those points are hexagon centres in the honeycomb.
Greg Egan /
npub12c…gd38p
2024-04-22 23:17:52
in reply to nevent1q…c78p
Author Public Key
npub12cuzzqzv8e8y7na77a9zv47mx2v6pec60qs5h7takzmv5p0mw0fsmgd38pPublished at
2024-04-22 23:17:52Event JSON
{
"id": "959730d956dd95a45fc69f0b7391de412ec6c75cbde023b6988c721509ea4dde",
"pubkey": "563821004c3e4e4f4fbef74a2657db3299a0e71a78214bf97db0b6ca05fb73d3",
"created_at": 1713827872,
"kind": 1,
"tags": [
[
"p",
"563821004c3e4e4f4fbef74a2657db3299a0e71a78214bf97db0b6ca05fb73d3"
],
[
"p",
"9a6a1a8eefd0b53d7e0c966ab35bd904151246f03b1be98fa0d2d0eeb4940320"
],
[
"p",
"2db431c8bab241109ce32e5b373c722c601c136c4ad4eb847478105046a16dc9"
],
[
"e",
"e927aa4d34290f336b1067313a215f5f53f403a4e9bcbb5a021075610a038b85",
"",
"reply",
"9a6a1a8eefd0b53d7e0c966ab35bd904151246f03b1be98fa0d2d0eeb4940320"
],
[
"e",
"f6229c8b793bfee46a674f42534461cb9760b976045fe98c6307ba61711fc2fe",
"",
"root",
"9a6a1a8eefd0b53d7e0c966ab35bd904151246f03b1be98fa0d2d0eeb4940320"
],
[
"proxy",
"https://mathstodon.xyz/@gregeganSF/112317423440287756",
"web"
],
[
"proxy",
"https://mathstodon.xyz/users/gregeganSF/statuses/112317423440287756",
"activitypub"
],
[
"L",
"pink.momostr"
],
[
"l",
"pink.momostr.activitypub:https://mathstodon.xyz/users/gregeganSF/statuses/112317423440287756",
"pink.momostr"
],
[
"-"
]
],
"content": "–3/2 is the dot product between two nearest neighbours among the set of points on the hyperboloid whose 2×2 matrices have Eisenstein integer entries.\n\nSo this is consistent with your guess that those points are hexagon centres in the honeycomb.",
"sig": "24af2faaa6ce97adccbdda13376f677019f34666ff4b9f06fb27c1d38f06c352deb4853dda05f5352ac8a5e4ebcc209a60931db5ab66d7fba324e76177102eeb"
}