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From: David Entwistle <qnivq.ragjvfgyr@ogvagrearg.pbz>
Newsgroups: rec.puzzles
Subject: Re: Orange stacks
Date: Mon, 21 Jul 2025 07:46:50 -0000 (UTC)
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On Tue, 15 Jul 2025 11:28:23 -0000 (UTC), Richard Tobin wrote:

> This wikipedia page makes it explicit:
> 
> https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres

Thanks. Also of particular interest is:

https://en.wikipedia.org/wiki/Kissing_number

Regarding the packing of twelve equally sized spheres in three dimensional 
space, it includes the following comment: "In fact, there is so much extra 
space that any two of the 12 outer spheres can exchange places through a 
continuous movement without any of the outer spheres losing contact with 
the center one." That is something I had failed to appreciate and my go 
some way to explain my confusion. My vision of a similarity to the 
tetrahedral carbon lattice, you may have seen at school during physics and 
chemistry lessons, is wrong. Or, at least, incomplete.

I now have this Conway, Sloane book on order:

<https://books.google.co.uk/books/about/
Sphere_Packings_Lattices_and_Groups.html?id=hoTjBwAAQBAJ&redir_esc=y>

-- 
David Entwistle