# Packing them in

### Sep 15, 2021

*Reading time: 2 minutes*

How can

npoints be distributed on a circle such that they maximize the minimum distance between any pair of points?

Of course! Don’t be daft, this is easy!

So far so primary school! Next!

How can

npoints be distributed on a sphere such that they maximize the minimum distance between any pair of points?

I… Errr… I think…. I… Erm… Can’t be that hard!?

Actually it all gets a bit tricky - the problem having given both Plato and Euler some sleepless nights. As a result of this pondering I now have a new favourite contemporary mathematician, Neil Sloane, who rather brilliantly has devoted a reasonable chunk of life to looking at this. He maintains a set of tables with all known solutions. Reading around this (and the related Thomson Problem) gave me an idea - can we create weird bounding geometry based upon Professor Sloane’s spherical packing codes?

### Demo

Presenting the (lets be honest - rather less than useful and not very catchily titled) Turtlestack NX Custom Feature - the ‘N Face Bounder’…

Frankly, you are more likely to want a bounding box or convex hull generated against your geometry, which NX can already do! That said I think there *might* be a role for this in generating *packable* shapes to encompass irregular forms? Perhaps if you chose the packing arrangement which would lead to a Platonic solid when bounding a sphere you might get nice stackable forms even for ‘irregular’ contents?

*Paul Booth*