Dihedral Group D3, Equilateral Triangle, Symmetries

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The Dihedral Group D3, Equilateral Triangle, Symmetries Given an equilateral triangle ABC, in how 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. Make a table and see how things are related. Then talk about them. There are two versions for both the top and the bottom part. They can be mixed and matched (A-B) for a model set. References 1. https://en.wikipedia.org/wiki/Dihedral_group_of_order_6 2. http://mathworld.wolfram.com/DihedralGroupD3.html