# Quick definition question: Dihedral group

1. Aug 8, 2012

### srfriggen

A dihedral group of an n-gon denoted by Dn, whose corresponding group is called the Dihedral group of order 2n?

What I gather from that is a square has 8 symmetries, an octagon has 16, a hexagon 12, etc?

2. Aug 8, 2012

### marschmellow

Yep, you got it.

3. Dec 25, 2013

### LagrangeEuler

When I do reflection in square do I need to put numbers and that do reflection for particular site of square. Is there some easiest way to find multiplication table of $D_4$?

4. Dec 25, 2013

### R136a1

Let $R$ be a rotation and $S$ a reflection. Use the relations $S^2 = 1$, $R^4 = 1$ and $SR = R^3S$. Using this you can find the multiplication table easily.