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From: Wei Zhang <zweig.scripps.edu>

Date: Mon, 23 Jul 2007 17:07:36 -0500

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

Received on Wed Jul 25 2007 - 06:07:24 PDT

Date: Mon, 23 Jul 2007 17:07:36 -0500

Ilyas Yildirim wrote:

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

Received on Wed Jul 25 2007 - 06:07:24 PDT

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