Mathematics
Symmetry Groups of Regular Polygons and Platonic Solids
Quick fact
The symmetry group of a regular n-gon is called the dihedral group Dn and has exactly 2n distinct symmetries: n rotations and n reflections. The symmetry groups of the five Platonic solids are among the finite groups that never appear as symmetry groups of any object in three-dimensional space, a fact linked to the classification of finite simple groups.
Why this is interesting
An equilateral triangle looks the same after a 120° turn or a flip—but how many total moves can you make and still have it look exactly the same? That count, and the structure that underlies it, is the symmetry group.