# Group theory, dihedral group

Why we study dihedral group? Please tell Real life example of dihedral group. I know this group mathematically.

From the comments: Actually I am going to tell about dihedral group to friends. So in introduction to dihedral group I have to tell the use of dihedral group in practicle life.why we need dihedral group. From where this originate.

• This question is unclear and somewhat unmotivated. What do you mean be a real life example? If you want somebody to point at a structure in the universe with dihedral symmetry that is easy, but easily too broad. Would you like such an answer? We have had quality threads about "real life" applications of group theory. Would those help you? – Jyrki Lahtonen Nov 23 '15 at 9:20
• Actually I am going to tell about dihedral group to friends. So in introduction to dihedral group I have to tell the use of dihedral group in practicle life.why we need dihedral group. From where this originate. – user270371 Nov 23 '15 at 9:25
• One possibly related thread and another. Not really specific to dihedral groups. But thanks for the comment. It does clarify your needs. – Jyrki Lahtonen Nov 23 '15 at 9:45
• It makes no sense to tell your friends about the meaning of the dihedral group before telling them about groups and symmetries in general (see Jyrki's links). Perhaps this has nothing to do with your friends, but just to understand more about dihedral groups. If so, you should pose a question, which is more detailed. – Dietrich Burde Nov 23 '15 at 10:24
• When I've googled dihedral group, uses I've find for example maa.org/sites/default/files/images/upload_library/4/vol1/… where is cited that the group is used in the classification of molecules and crystals, too to made designs.I'm agree with Burde's comment. – user243301 Nov 23 '15 at 10:33

There the viewer sees a pattern $P$, its reflected image, the reflection of the reflection et cetera. Altogether the view consists of parts like $g(P)$, where $g$ ranges over a dihedral group. Or a bigger group - all depending on how many mirrors are used (with two mirrors you get the dihedral group).