Dihedral Group D3, Equilateral Triangle, Symmetries

####Dihedral Group D3, Equilateral Triangle, Symmetries

Given an equilateral triangle ABC, in how many many different ways can one map it onto itself, by rotation or reflection (flipping)? There are six such mappings, which are collectively called the dihedral group D3 with order 6.

Of course, we can ask the same questions about a square, a regular pentagon, etc. These symmetries are very interesting. If we ignore the term, dihedral group, the problem can be posed to young children. Ma