Most mathematical objects have things that can be said about them that are always true. These are called properties. All polygons (convex and star polygons) can be rotated in place by some angle and still look the same—in other words, they're all rotationally symmetric. For example, a square could be rotated a quarter turn, and it would look the same as before. Another way of seeing this property is that any polygon can have a circle drawn around it, touching all its points, and the polygon's points are evenly spaced around the circle. A polygon can also have a circle drawn inside it, touching all its edges (but not overlapping), and the places where the circle touches the polygon are also evenly spaced. The centers of the two circles drawn are in the same place. This proves that a regular polygon is rotationally symmetric.
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