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From: richard@cogsci.ed.ac.uk (Richard Tobin)
Newsgroups: rec.puzzles
Subject: Re: Orange stacks
Date: Tue, 15 Jul 2025 11:28:23 -0000 (UTC)
Organization: Language Technology Group, University of Edinburgh
Message-ID: <1055e0n$1eqj6$1@artemis.inf.ed.ac.uk>
References: <104tudv$274e7$1@dont-email.me> <10527u5$391km$1@dont-email.me> <1052r4u$1dds7$1@artemis.inf.ed.ac.uk> <1054sl4$3u0lv$1@dont-email.me>
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Originator: richard@cogsci.ed.ac.uk (Richard Tobin)

In article <1054sl4$3u0lv$1@dont-email.me>,
David Entwistle  <qnivq.ragjvfgyr@ogvagrearg.pbz> wrote:

>I'm still struggling with the idea the structures of the square-based and 
>triangular-based pyramids are the same.

They are, just at different orientations.

This wikipedia page makes it explicit:

https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres

Both are face-centred cubic (FCC).  The diagrams labelled FCC on the
wikipedia page show the two orientations.

-- Richard