I’m not sure this question belongs here as I might think it needs to go into Grasshopper. I have a sphere that needs to be covered by hexagons of a specific size. The sizes are 25, 50, 100, 150 inscribed circle.

I’m hoping to to find the two options. The first is where as many as possible will be covering the sphere. Preferably in a chaotic order. The second is to create a way to cover the sphere in the hexagons and step down to a smaller tile if necessary.

Great thanks for any help on this question. Cheers.

If sharing edges, then you wouldn’t be able to use only hexagons, you’d need some faces with fewer sides (for example 12 pentagons).

If you want to prescribe the sizes though, they can’t all be sharing edges, since the edges step between the different sizes, so I guess you mean with gaps?

I also don’t understand the second part of your question about “cover the sphere in the hexagons and step down to a smaller tile if necessary”

Thank you for the reply. Sharing edges is not important. By “step down” I mean a smaller size if the bigger size doesn’t fit. It must be made of the sizes I indicated though. A kind of chaotic “circle packing” could also be nice.

Here’s something to get you started.
It actually packs circles with a given number of each of the given sizes, then places hexagons inside them.
Doing the packing on the hexagons directly could give denser arrangements - it would be a bit more complex to set up (though I think it would be possible).