Dihedral symmetry in three dimensions
Imagine you have a toy airplane with two wings, like the letter "W" in shape. Now imagine you can rotate the airplane in such a way that both the wings are facing up and down at the same time. This ability to rotate the airplane and still have it look the same is called dihedral symmetry.
In three dimensions, dihedral symmetry is when an object can be rotated around an axis in such a way that it looks the same after a certain degree of rotation. This rotation can happen multiple times around the same axis.
For example, imagine a cube. If you rotate the cube around one of its diagonals, you'll see that there are certain degrees of rotation where the cube looks the same as it did before. Specifically, after rotating the cube by 90, 180, or 270 degrees around this diagonal axis, it will still look the same.
This property of being able to rotate an object and have it look the same is useful in many fields, including chemistry and crystallography, because it allows us to predict certain physical properties of molecules and materials.
In three dimensions, dihedral symmetry is when an object can be rotated around an axis in such a way that it looks the same after a certain degree of rotation. This rotation can happen multiple times around the same axis.
For example, imagine a cube. If you rotate the cube around one of its diagonals, you'll see that there are certain degrees of rotation where the cube looks the same as it did before. Specifically, after rotating the cube by 90, 180, or 270 degrees around this diagonal axis, it will still look the same.
This property of being able to rotate an object and have it look the same is useful in many fields, including chemistry and crystallography, because it allows us to predict certain physical properties of molecules and materials.
Related topics others have asked about: