The picture shows the pentagonal star in green, and the circumscribed blue pentagon and the inscribed red pentagon. F is the centre of both pentagons and also the centre of a circumscribed circle. The clockwise rotation angle for symmetry is 72º=360/5. There are 5 positions for rotational symmetry. The set of rotations is {R₇₂, R₁₄₄, R₂₁₆, R₂₈₈, R₃₆₀}. R₃₆₀ could be omitted because it’s the identity rotation, I or R₀, that is, no rotation. For example, vertex A can be rotated to B, C, D or E, and a further rotation just puts A back to where it started.
ROTATION MULTIPLICATION TABLE
