Point groups in two dimensions
Okay kiddo, let me explain what point groups are in simple terms.
Imagine you have a piece of paper and a crayon. Now draw a shape on the paper, like a star or a square. This shape is known as an "object".
Now, let's think about what happens when we rotate this object. If we turn it a little bit, it might look slightly different but it's still the same object.
But if we turn it a lot, it might look completely different. That's because a shape can have different symmetries or patterns when it's rotated.
A point group is just a fancy way of talking about all the different symmetries an object can have when it's rotated in two dimensions.
For example, imagine a square. If we rotate it by 90 degrees, it looks exactly the same. That's called a "rotational symmetry" of order 4 because it takes 4 rotations to get back to the original shape.
But if we flip the square over, it looks different. That's called a "reflection symmetry".
So, this square has two different symmetries - rotation and reflection - which means it belongs to a certain point group.
Different shapes have different point groups with different types of symmetries. But basically, a point group just tells you all the different ways you can rotate or reflect an object in two dimensions while keeping it looking the same.
Does that make sense?
Imagine you have a piece of paper and a crayon. Now draw a shape on the paper, like a star or a square. This shape is known as an "object".
Now, let's think about what happens when we rotate this object. If we turn it a little bit, it might look slightly different but it's still the same object.
But if we turn it a lot, it might look completely different. That's because a shape can have different symmetries or patterns when it's rotated.
A point group is just a fancy way of talking about all the different symmetries an object can have when it's rotated in two dimensions.
For example, imagine a square. If we rotate it by 90 degrees, it looks exactly the same. That's called a "rotational symmetry" of order 4 because it takes 4 rotations to get back to the original shape.
But if we flip the square over, it looks different. That's called a "reflection symmetry".
So, this square has two different symmetries - rotation and reflection - which means it belongs to a certain point group.
Different shapes have different point groups with different types of symmetries. But basically, a point group just tells you all the different ways you can rotate or reflect an object in two dimensions while keeping it looking the same.
Does that make sense?
Related topics others have asked about: