[seqfan] Re: Maximal number of touching points between unit spheres (fwd)

Graeme McRae graememcrae at gmail.com
Tue Mar 13 22:41:46 CET 2018


The five points representing the vertices of a pair of tetrahedrons joined
at one face:
A=(-.5,-sqrt(3)/6,-sqrt(6)/12)
B=(.5,-sqrt(3)/6,-sqrt(6)/12)
C=(0,sqrt(3)/3,-sqrt(6)/12)
D=(0,0,sqrt(6)/4)
E=(0,0,-5*sqrt(6)/12)
The distances AB, BC, CA, DA, DB, DC, EA, EB, EC are all 1.


--Graeme McRae
Palmdale, CA

On Mon, Mar 12, 2018 at 1:25 PM, rkg <rkg at ucalgary.ca> wrote:

> Dear Karoly,
>             Perhaps you can answer this?   R.
>
>
> ---------- Forwarded message ----------
> Date: Mon, 12 Mar 2018 13:44:58 +0000
> From: Richard J. Mathar <mathar at mpia-hd.mpg.de>
> Reply-To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> To: seqfan at seqfan.eu
> Subject: [seqfan] Re: Maximal number of touching points between unit
> spheres
>
> Related to http://list.seqfan.eu/pipermail/seqfan/2018-February/018394.
> html
>
> My explicit computation for clusters of spheres centered on the f.c.c.
> lattice gives 0,1,3,6,8,12,15,... for A214813: a discrepancy at
> a(5). [I checked that my number of configurations equals A038173.]
>
> There is a sentence in Bezdeks "Contact numbers..." Disc. Comput. Geom
> (2012)
> saying "if this were true,... if would follow that C_fcc(5)=9", which
> might be the reason why currently a(5)=9.
>
> So the question is: is A214813(5)=9 correct, perhaps referring to
> unconstrained/disordered sphere
> packings, or do we need to change either the definition or the numbers, or
> is my
> analysis just wrong and missing configurations with 5 spheres on the f.c.c.
> lattice? Can anyone provide the sphere center coordinates of 5 spheres
> in a f.c.c. lattice with 9 contacts, as claimed in A214813?
>
> Richard
>
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