PS: PingYou is hiring
budden@pingyou.com

Eyeballing some of the 2000+ tetrahedra packing records PingYou holds on polyhedrainpolyhedra.wiki

If you pay no attention to anything else I ever tweet, pay attention to this one construction.

It is the sum of all math, truth and beauty in one weird-cube. Pinky promise.

Again. The rest of the exercise I leave to the reader

Read the two headers *slowly* before closing this tweet

Okay but hear me out

I fixed Claude's attempt with the same prompt

Better luck next time bros those shell companies have strong false address game

A couple of these are superceded now but for folks who are more into arithmetic than geometric results:

pingyou.com/papers/erdos-1…
pingyou.com/papers/erdos-2…
pingyou.com/papers/erdos-2…
pingyou.com/papers/erdos-3…
pingyou.com/papers/erdos-3…
pingyou.com/papers/erdos-7…

... Sorry that was kinda mean

Some more fun 3D packing records from the 2000+ we submitted today

Okay pretty chuffed with this record

Busy week! PingYou also has validated records for self-packing of each platonic solid

@AlejandroZarUrd I'm conscious I've just spammed your agents with 1500+ candidates to verify. Shoot me a message if you need PY to sponsor your token bill today 😅

PingYou has has 68 square packing records confirmed, including 3 against our own constructions

Here's a serious question. Has anyone proven that "2 cubes" is the worst optimal packing of a 3D polygon into itself? Because I strongly suspect it might be

Man pairs of tetrahedra are brutal. Worst case best packings for platonic (left) and archimedean (right) solids

NO! 2 icosahedra in a tetrahedron yields ~24.95% bound
Wtf is going on here

(loosening the criteria to "N M-gons in a P-gon")

Rookie numbers. Two tetrahedra in a dodecahedron. 15.5% bound

"Budden's packing conjecture"

(convex polyhedra only)