Is there a general test for chirality?

Vorde

I have been wondering:

Given an arbitrary geometric shape is there a sequence of tests I can perform on individual parts of the shape to determine whether or not it is achiral?

I was hoping for something a little less trivial that simply seeing if the mirror image could be adjusted to match the original, more something along the lines of looking at the composition of the shape itself.

Gratias.

Bacle2

You can try polynomial invariant, like Jones, or Homfly, but this is not an iff way, i.e., achiral knots may be assigned the same polynomial (usual problem one has with algebraic topology).

EDIT: Sorry, I did not read carefully-enough; I think you may be looking for a different approach.

Vorde

I am way, way, outside of my knowledge zone here, so I apologize if everything I say is wrong.

I wasn't thinking achiral with knots as much I was with just plain shapes like sticks or hands. I sort of was thinking that it seemed to me that if you took a shape and found an arbitrary center. The shape would be chiral if you could rotate the shape such that it was asymmetrical in two separate dimensions.

I'm pretty sure I've falsified that idea but I was wondering if there was a geometrical approach similar to what I tried to do that works.

Bacle2

No need to apologize for (the possibility of ) being wrong; main thing is to be curious and open-minded.

Let me see if I get what you're asking:

So you want to see if, say a hand , to be isotopic to their respective mirror images?

And then you want to see if you can find a point p in the shape rotate the shapes along

p, the rotated shape will be symmetric (meaning you can decompose it into two

parts that are mirror images of each other)? If I understood you well, a hand

cannot be rotated into being composed of two disjoint mirror images.

Vorde

What I meant was to ask is there a simple geometric process from determining if an arbitrary shape is achiral or not.

I don't think that my idea about the rotations works, because I think I found a shape which is achiral yet satisfies my rotations process, but I'll think about that more tomorrow.

I'm just wondering if a process exists, I doubt mine is the correct one.

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Bacle2 Recognitions: Science Advisor	You can try polynomial invariant, like Jones, or Homfly, but this is not an iff way, i.e., achiral knots may be assigned the same polynomial (usual problem one has with algebraic topology). EDIT: Sorry, I did not read carefully-enough; I think you may be looking for a different approach.

Vorde Recognitions: Gold Member	What I meant was to ask is there a simple geometric process from determining if an arbitrary shape is achiral or not. I don't think that my idea about the rotations works, because I think I found a shape which is achiral yet satisfies my rotations process, but I'll think about that more tomorrow. I'm just wondering if a process exists, I doubt mine is the correct one.