From: "dick_fischbeck" ... VE, ... than ... In SPHERE form, yes, they have to: the volume taken up by the spheres is the same (there are 13 spheres in both),...
... From: "dick_fischbeck" <dick_fischbeck@...> ... Yes, I can envision that. It's as if you stuck a new sphere in the center of the pack, forcing the...
... But composed of multiple sphere sizes, hence "anything's possible." Seems to me unless we use one size sphere, we'd be shootin' in the dark. Peace JB ...
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Lee Bonnifield
lee@...
Jul 2, 2002 5:55 am
... center, ... I think you do not mean to define icosahedro(not) to include the requirement that the 12 must be "in contact" with a 13th. ... I don't have a...
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Lee Bonnifield
lee@...
Jul 2, 2002 5:55 am
... I don't think that's what he meant. If you add a sphere to the OUTSIDE of the shell, several spheres near it that WERE on the outside are now on the ...
... Exactly. The exterior of the big sphere is made of a 2-d closest packing of little spheres. All exterior sphere are equidistance from a center. This shell...
... I don't see any reason to except a 12 around 1 packing from being an icosa just because it has a "square" face. I still see 2 triangles between those 4...
... John, what makes an I-not different from an icosa? What is the origin? The missing 6 edges? Maybe because of the nucleus? I propose we take Kirby's...
... not ... otherwise ... Thank you. (*grin*) Note, for those interested in "either-or" situations (like polarization), that a space containing some of these...
From: "Lee Bonnifield" ... to ... existing ... same ... 12 ... requirement ... Right, OK; it's a fuzzy area. I tend to use I(not) mostly in reference to 13...
6898
Lee Bonnifield
lee@...
Jul 3, 2002 6:49 am
... icosahedron: a solid figure having 20 faces I don't want to change that centuries old definition (from Greek ~eikosi = 20) do you? If a 12-around-1 has a...
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Lee Bonnifield
lee@...
Jul 4, 2002 5:38 am
... Does this mean the same thing as your last sentence: For a cluster of 100s of spheres, in general more than one sphere must be added to the interior before...
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Lee Bonnifield
lee@...
Jul 4, 2002 5:38 am
... The subject matter is not fuzzy, but your usage is fuzzy. ... I've always encouraged you to invent neologisms, and as long as you do I'll try to use them...
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Lee Bonnifield
lee@...
Jul 4, 2002 5:38 am
... OK, I see he DID mean what you said. You say the "whole" pack moves, and "no sphere stays in place if a sphere is added" and "shuffling all the spheres in...
Does someone have the formula for the total number of circles in a hexagonal packing, according to frequency? I can't find it. I have the one for total spheres...
Is anyone familiar with this 5F^n relationship? Its new to me. Dick http://www.rwgrayprojects.com/synergetics/s09/p8280.html 982.80 Closest Packing of...
However, for a high ... Okay, that's pretty close. The shell count grows faster than the interior sphere count for clusters _under_ a certain size, which I ...
Naive alert. In circle packing, the area of a circle of circles seems to be radius times the circumference. Circumference equals the number of circles in the...
From: "Lee Bonnifield" Subject: Re: [synergeo] Re: sphere clusters ... the ... (*grin*) Thanks for the note on that, Lee. It seems he meant a little of...
Proposed cutoff for a "neighbor" sphere: Given one sphere, and given any number of other, identical spheres arrayed around it in any pattern at all, and given...
JB, I would suggest that a way to initially define a "neighbor" would be, given some sphere, any sphere, then its "nieighbors" would be any other spheres...
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Lee Bonnifield
lee@...
Jul 5, 2002 6:57 pm
... You must be assuming a particular packing density, since by definition a variation in density (with the same number of spheres) produces a variation in...
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Lee Bonnifield
lee@...
Jul 5, 2002 6:57 pm
... This looks OK to me, as long as it is in the context of a 3-D Euclidean metric. If the space were other than those (continuous) dimensions, the kissing...
JB, I mixed up my radius and diameter calc for a "neighbor"... Oh yes, I have the formula here...the diameter is twice as big as the radius, perhaps I should...
From: "Lee Bonnifield" Subject: Re: [synergeo] "neighbor" ... All ball-packings we've been doing have to be done within some metric we can "see." That's, most...
Offtopic By the way, Lee, I forget where you live? I'm readying myself for a truck-camping trip to Kentucky. Anywhere close? Peace JB jgbrawley@... ...
