What, if any, examples of the regular solids, dodecahedrons and icosahedrons, exist in nature?
I suppose then nature would not exist
In 2003, an apparent periodicity in the cosmic microwave background led to the suggestion, by Jean-Pierre Luminet of the Observatoire de Paris and colleagues, that the shape of the Universe is a finite dodecahedron, attached to itself by each pair of opposite faces to form a Poincaré sphere. ("Is the universe a dodecahedron?", article at PhysicsWeb.) During the following year, astronomers searched for more evidence to support this hypothesis but found none.
Found this on Wiki. sounds like idle speculation to me. Who comes up with this stuff....
Some time ago I have gone trough J.P.Luminet's book "Lunivers chiffonné" and als through the book of Janna Levin "How the universe got its spots". For several reasons I don't see a possibility for a universe embedded in nothing at all (IMO "nothing" and no space never existed or will ever exist).
But I misunderstood the question and that was why I made my post. The reason why I did that is because I wanted to state that pure mathematical entities like circles and dodecahaedrons, ideally, do not exist at all in nature. What nature shows are examples of physical things whose form can aproximately be described by such mathematical forms. Mathematics is very helpful to a certain degree to explain reality, but I see that somewhere the mathematical package does'nt fit anymore, e.g. singularities in GR, or broken symmetries to take into consideration in quantumgravity?? At least then one has to adapt the mathematical package but IMO it will always be only just language and never reality. Even physics only consist of, ever to be adapted, physical models and will never be the autonomous reality itself.
Kind regards Hurk4
Better forget everything I said here. It really was no answer to the question!
My chemistry professor did a ton of research on carborane cages that had dodecahedron and icosohedron shapes.
Are they present in nature?
(I assume that fullerenes are all synthetic.)
Half the time you stack identical spheres tightly, they pack in precisely the same pattern as a dodecahedron. The dodecahedron is basically the first Brillouin zone of one of the two natural sphere-packing patterns.
Except I think the Brillouin zone involves inverse lattices. Oh well, I never did like solid state, and that was decades ago. If you know what a Brillouin zone is, you'll see my point, even if I haven't got it quite right. I mean the minimum volume construct of perpendicular bisector planes between each point in the lattice and the central reference point of the figure.
That may be the best definition yet of a Brillouin zone. However, their existence remains theoretical, a conceptual tool.
So far the virus wins out.
Well, certainly in detectable amounts they're synthetic. But fullerenes are made by processes that don't require human intervention. Sort of.
What I mean is: fullerenes were detected, not deliberately produced. True, scientists had set up the circumstances wherein the carbon was heated and tossed about, but the fullernes created themselves by fluke.
"In molecular beam experiments, discrete peaks were observed corresponding to molecules with the exact mass of sixty or seventy or more carbon atoms. In 1985, Harold Kroto (of the University of Sussex), James Heath, Sean O'Brien, Robert Curl and Richard Smalley, from Rice University, discovered C60, and shortly after came to discover the fullerenes. "
If the right conditions were found, there is no reason why they would not be found naturally.
However, that's buckminsterfullerene. Dodecahedrane is what you're asking about, and it was synthesized.
Could molecules of single elements other than carbon (like silicon) form the aforementioned Platonic structures?
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