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Topic: Volume of a Geodesic Dome
Replies: 4   Last Post: Feb 20, 1999 4:31 PM

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John Sullivan

Posts: 14
Registered: 12/6/04
Re: Volume of a Geodesic Dome
Posted: Jul 8, 1995 5:06 PM
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In article <Pine.SUN.3.91.950629162842.8995K-100000@mace.Princeton.EDU>,
John Conway <conway@math.Princeton.EDU> wrote:
>On 28 Jun 1995, Your Name wrote:

>> Can any one describe for me how one would determine the volume of a
>> geodesic dome as a function of the number of sides it has? I've made the
>> assumption that all the sides are triangular with 60 degree angles.
>> - Jason Acker

> I'm afraid that there's no real answer to this question, because
>"geodesic domes" vary in shape. Also, it's seldom the case that
>all the triangles have the same shape; if you look carefully at the
>next one you see, you'll see they have slightly different sizes and
>shapes, and aren't all equilateral. ...
> (base times height)/3

John's comments are certainly valid, but I'd just like to point out
that we can estimate fairly well the volume of a geodesic dome made
of a large number N of triangles, each of which is nearly equilateral
(say all the side lengths are close to 1).

The total area of this dome will be $N\sqrt{3}/4$, if it is approximately
a sphere of radius $r$, then we must have $4\pi r^2 \approx N\sqrt3/4$,
and volume approximately $4\pi r^3/3$. We can solve for r and see
that this volume is about
(N \sqrt{3})^{3/2} / (48 \sqrt\pi)

-John Sullivan

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