Regular Triangle Symmetry Group Exploration
Complete the multiplication table for D4, the symmetry group of the square.
|(identity)||(rotation 90)||(rotation 180)||(rotation 270)||(reflection)||(reflection)||(reflection)||(reflection)|
The equilateral triangle
Analyze the symmetry group D3 of the equilateral triangle:
- How many elements are in this group?
- What is x = ? , x = ? , x = ?
- What is x ? , x ? , x ? , x ? , x ? , x ?
- 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.