Finding angle between two hexagonal planes

Question

I am looking to get angle between two hexagonal planes. I have coordinates of all 12 vertices (2 hexagons). Is there anyway I can find the angle between the planes. And also I have the information about the centers of each hexagonal plane.

You can see the two hexagons, I need to find the angle between them

Its a plane formed by six coordinates which forms a hexagon.It's like a benzene ring. — Adupa Vasista, Jun 24 '20 at 05:36
A plane needs only three points to be uniquely defined. The angle between the planes would be the same as the angle between the normals. — Andrew Chin, Jun 24 '20 at 05:37
Let's say the plane is a benzene ring and I need to find the angle between two benzene rings — Adupa Vasista, Jun 24 '20 at 05:38
@AndrewChin Thank you Andrew, I figured out that earlier, Is there anything to find the equation of plane using these coords. I am a little bit poor in math. I request to elaborate more on anything suggest. Thank you — Adupa Vasista, Jun 24 '20 at 05:39
Now that you know the method, you can definitely try to solve the problem. Edit your original question to show your work. — Andrew Chin, Jun 24 '20 at 05:41

Chris Culter · Accepted Answer · 2020-06-24T06:53:54.267

Having six coordinates actually makes the problem harder, because it's over-determined. Are these empirical measurements with some systematic noise? Is it possible that the rings are somewhat bent? If the answer is either question is yes, then you probably want to take some kind of average using all six points, rather than randomly choosing three and ignoring the other three.

Here's one way to find the normal vector of a plane fit to a point cloud: https://math.stackexchange.com/a/99317/87023

Edit: If you insist on assuming that the points lie on the same plane, then it's enough to choose three points. I still recommend using all six points, though. You can take the normal vector to points 1, 3, and 5, and also take the normal vector to points 2, 4, and 6. You expect these normals to be parallel, but if they're slightly off, then you can average them together, and treat that average as the normal to the hexagon. This procedure is ad-hoc but simple, and it has the advantage that it doesn't depend on where you start the labeling.

Once you have two normal vectors, you can use their dot product to compute the angle between them: https://math.stackexchange.com/a/654331/87023

No the rings are not bent. Are these empirical measurements with some systematic noise? I don't know about this, can you explain more. So Should I just choose three coords randomly and find the normal and then find the angle, that's it. ? — Adupa Vasista, Jun 24 '20 at 06:24
Measurements taken in the real world are never perfect. They're always a little bit off. I wouldn't choose randomly, if only because the result won't be repeatable. I'll add a compromise method to the answer. — Chris Culter, Jun 24 '20 at 06:48

Finding angle between two hexagonal planes

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