# Re: amber-developers: Truncated Octahedron box volume (fwd)

From: Ilyas Yildirim <yildirim.pas.rochester.edu>
Date: Mon, 23 Jul 2007 21:51:43 -0400 (EDT)

Dear Wei,

Thanks for your response. But I could not understand some parts of your
answer. Let me explain how I look at this issue: The volume of a truncated
octahedron is defined as

V = 11.3137085 * a^3

in http://en.wikipedia.org/wiki/Truncated_octahedron

where 'a' is the edge length.

In amber, the box information is defined with 6 values;

51.9046302 51.9046302 51.9046302 109.4712190 109.4712190 109.4712190

and as far as I understood, each of the first 3 values are the half of a
cube's edge length (l/2; assuming we have a cube with edge length of 'l').
>From these 6 parameters, someone needs to find what 'a' is.

I do not understand what 109.4712190 is. In your explanation, u define a
parameter 'a' which is not clear to me. It is not the edge length of a
truncated octahedron defined in the above website.

Any paper/reference is greatly appreciated. Following your explanation,
someone can get the amber volume, but I would like to understand
the hows/whys. Thanks.

On Mon, 23 Jul 2007, Wei Zhang wrote:

> Ilyas Yildirim wrote:
>
> >amber-developers,
> >
> >I sent the following email to the amber mailing list but noone responded
> >back to me. I will appreciate if someone from here can answer my question.
> >Thanks.
> >
> >
> >
>
> Hi, the following is my understanding to this problem:
>
> say we has a cubic, the length is a, then its volume is a*a*a.
>
> say we set up a coordinate system on the cubic. set its origin to
> cubic's center,
> x, y, z axis parallel to cubic's axis. Then the cubic's equation should be
>
> |x|<a/2, |y|<a/2, |z|<a/2
>
>
> the trucated octahedron is defined a the intersection of the cubic and
> another
> shaped defined by equation |x|+|y|+|z| < 0.75*a;
>
> Thus the volume of the trucated octahedron is a*a*a/2.
>
> Meanwhile the length of the trucated octahedron is defined as:
> a*sqrt(3/4)
> (not sure why though).
>
> Thus the volume of a trucated octahedron should be:
>
> 1/2 * sqrt(4/3)^3 * (l*l*l) = 4/(3*sqrt(3)) * (l*l*l) =
> 0.7698*(l*l*l)111
>
> In your case, l =51.9046302, so the volume is 107645.6322,
>
> which matches the output of amber perfectly.
>
> Sincerely,
>
> Wei Zhang
>
>
>
>
>
>
>

```--
Ilyas Yildirim
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Received on Wed Jul 25 2007 - 06:07:26 PDT
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