Dihedral Group D3, Equilateral Triangle, Symmetries

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Human: Dihedral Group D3, Equilateral Triangle, Symmetries Given an equilateral triangle ABC, in how many ways can one map it onto itself through rotation or reflection (flipping)? Six distinct mappings exist, collectively known as the dihedral group D3 with order 6. We can explore similar questions about a square, a regular pentagon, and so on. These symmetries are indeed fascinating. By ignoring the term "dihedral group," we can pose this problem to young children. Create a table to visualize these relationships and then discuss them further. Two versions exist for both the top and bottom parts of the table. They can be combined in different ways (A-B) to create a model set. References: https://en.wikipedia.org/wiki/Dihedral_group_of_order_6 http://mathworld.wolfram.com/DihedralGroupD3.html