eli5: Why 360 degrees divided by the order of symmetry give us the magnitude of rotation (angle of rotation?)

Question

eli5: Why 360 degrees divided by the order of symmetry give us the magnitude of rotation (angle of rotation?)

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Answer 1

That follows from what the definition of “order of symmetry” is. A full rotation is 360 degrees. The order of symmetry is how many times you would return to your original object while doing one rotation.

If you have a square, with an order of symmetry of 4, you’re going to see the same square if you rotate it 90 degrees, or 180 degrees, or 270 degrees. 360/4 = 90.

If you have a decagon or a ten-pointed star, with an order of symmetry of 10, rotating it 36 degrees would result in the same shape.