Is there any perfectly symmetrical 3-way division in nature?

Question

I mean take some object, and have it split into 3 identical thirds.
Same questionfor 4,5,6 etc.

I do not mean any mathematical process.

Thanks for answers so far, but I stressed "perfectly" symmetrical and I mean it. Approximation is of no use to me in this context.

In the common world there are a lot of things we regard as being symmetrical which are not truely symmetrical. Books will use the word and we understand its meaning, but in all cases known to me there are differences. e,g, the human body is not truely bilaterally symetrical, the heart, pancreas, liver and other organs are not central.

Echinoids do not truely have 5-fold symmetry, but something approaching it. (I have collected and drawn these by the way.)

No examples of how one might divide something in theory are of any use. That is just mathematics. Numbers are artificial.

Consider buying 3 oranges. They might all look the same, but their weights might vary by perhaps 2%. So they are not the same.

Consider 3 coins. Perhaps they were made in the same press. Perhaps they have similar mass within 0.00001%. They are still not identical.

Answer 1

This is a good question. When I read the answer about the 3 petal flowers, I was skeptical - not about whether or not there are such, but about whether they have true trilateral symmetry. I don't have any 3 petal flowers, but I do have clover in my yard. I'm presently looking at a sample. Sure enough, their trilateral symmetry is superficial. First of all, the main stem has bilateral symmetry; there is is a groove running its length, giving the cross section a kidney or heart shape. Second, the three leaflet stems that radiate out from the top of the main stem are not all the same length. The one opposite the main stem groove is about 50% longer that the other two. And thirdly, the leaflet with the longer stem is noticeably rounder than the other two. So, a clover has bilateral symmetry like many things. This is not surprising because clover, like many plants, is a dicot (referring to its class). Dicots are plants that grow from seeds with bilateral symmetry.

Some echinoderms have true hexagonal symmetry. 6 is divisible by 3, so this technically qualifies. The most familiar echinoderms are the starfish, which have 5-fold symmetry, but the six-armed Luzon sea star has 6. I can't think of anything living with *only* three fold symmetry, though, in the sense of not also having a higher order symmetry too like the above sea star or even full axisymmetry.

As for minerals, hexagonal symmetry is common. The molecules that make them up can join up in triplets with trilateral symmetry while in solution, but such triplets join up into the hex cell units as they crystalize further.

Answer 2

If you're going to split hairs nothing can be that symmetrical, the coins you mention are to 5 decimal places how exact do you want to be?

Answer 3

The sun.

Any perfect circle can be divided into an almost infinite number of identical portions, so long as you divide it through the centre.

Answer 4

Sure. There are many flowers that have only three petals.

Like the Trillium.

Answer 5

I think you need to be more specific. Any prism can be split into identical thirds.