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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
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

*>
*

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').

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 --------------------------------------------------------------- - Department of Chemistry - - - University of Rochester - - - Hutchison Hall, # B10 - - - Rochester, NY 14627-0216 - Ph.:(585) 275 67 66 (Office) - - http://www.pas.rochester.edu/~yildirim/ - ---------------------------------------------------------------Received on Wed Jul 25 2007 - 06:07:26 PDT

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