TITLE: Can I represent groups geometrically?
QUESTION [33 upvotes]: I have just taken up abstract algebra for my college and my professor was giving me an introduction to groups, but since I like geometric definitions or ways of looking at stuff, I kept thinking, "How do you represent a group geometrically in a space?" Is there any way of representing it?

REPLY [9 votes]: You might find interesting a computer app called Group Explorer.
The app provides visualizations of 59 groups. Additional groups are available as separate downloads.
Some screenshots: