Question

summarize the rotations that carry a regular pentagon onto itself. in 3 sentences

Answer 1

A regular pentagon is invariant under five rotations about its center: by 0°, 72°, 144°, 216°, and 288° (equivalently k·72° or k·2π/5 radians for k=0,...,4). Each nontrivial rotation cyclically permutes the five vertices (a 5-cycle). These rotations form a cyclic group of order 5 generated by the 72° rotation.