# Regular Triangle Symmetry Group Exploration

From EscherMath

**Objective:**
Understanding the finite symmetry groups.

## The square

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*.

**Handin:**
A sheet with answers to all questions.