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polyhedron radius

 
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polymorphic



Joined: 17 Feb 2008
Posts: 26

PostPosted: Mon Oct 13, 2008 6:42 pm    Post subject: polyhedron radius Reply with quote

Hi Rob,

It appears the value you give for a polyhedra radius is the maximum distance between centroid and the vertices.

Is this the excepted definition of polyhedron radius?

My thinking is that this radius, if swept out as a sphere would contain every possible point in the polyhedra. Faces and edges could not surpass this distance.

Roger
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robertw
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Joined: 10 Jan 2008
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Location: Melbourne, Australia

PostPosted: Tue Oct 14, 2008 1:10 pm    Post subject: Reply with quote

Aren't these the same definition? Can you give an example?

Rob.
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polymorphic



Joined: 17 Feb 2008
Posts: 26

PostPosted: Tue Oct 14, 2008 11:32 pm    Post subject: Reply with quote

Actually I was just guessing what you did and why you chose it.

Take the built in icosahedron. Scale it by 2.0 on the 2-fold axis.

Then measure the longest diagonal. It is 11.21688.

You report the radius as being 5.60844 which is 11.21688 / 2.

I was just observing that this radius would always encompass (or contain if you will) the stretched icosahedron at any rotation.

Roger
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robertw
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PostPosted: Wed Oct 15, 2008 9:11 am    Post subject: Reply with quote

OK, and yes your guess is right. I don't know that the meaning of "radius" without any qualifiers is necessarily well-defined for polyhedra. Things like inradius, midradius and circumradius are defined for regular polyhedra and some others, but just radius on its own probably isn't, but I'd consider it to be as you said, just large enough to contain all parts of the polyhedron. I don't take infinite parts into consideration however. It wouldn't be very useful if I did.

Rob.
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