Regular Triangle Symmetry Group Exploration
Complete the multiplication table for D4, the symmetry group of the square.
|E (identity)||R (rotation 90)||R2 (rotation 180)||R3 (rotation 270)||M1 (reflection)||M2 (reflection)||M3 (reflection)||M4 (reflection)|
The equilateral triangle
Analyze the symmetry group D3 of the equilateral triangle:
- How many elements are in this group?
- What is M1 x M1 = M12? , M2 x M2 = M22? , M3 x M3 = M32?
- What is M1 x M2? , M2 x M1? , M3 x M1? , M1 x M3? , M3 x M2? , M2 x M3?
- How do rotations behave?
- Can you spot C3 as a subgroup of D3? What is it?
- Find all subgroups.
- Write out a multiplication table for D3.