# Plane Groups

Dexter Perkins
,
University of North Dakota
Author Profile

#### Summary

Studying plane groups is a good way to introduce crystal systems, point groups, lattices, symmetry operators, etc. All is in 2-D, but it is easy to tell students that the principles are the same in 3-D. I provide, here, a PDF document with more than 60 images for instructors to use. For those who like to make changes, the PDF document was created from individual EPS files. This means that the files can be opened in Adobe Illustrator, Corel Draw, etc., and modified to fit your own needs.

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## Context

#### Audience

I use this in my sophomore Mineralogy course.

#### Skills and concepts that students must have mastered

There are no requirements -- this material can be used to introduce symmetry even if students don't know what it is.

#### How the activity is situated in the course

This is one of many in-class activities that we do. We do this about 2/3 of the way through the semester.

## Goals

#### Content/concepts goals for this activity

After looking at the graphics and completing some in-class activities students will be able to explain the following and how they relate to each other:
• crystal system
• unit cell
• lattice
• lattice points
• symmetry groups
• symmetry operators

#### Higher order thinking skills goals for this activity

In particular, students develop the visualization skill needed to see symmetry.

## Description of the activity/assignment

This is a lengthy PDF document (60 pages+) about plane groups and symmetry. It includes colorful images of each of the 17 plane groups, in several different forms. Additionally, there are some summarizing graphics that show unit cells, lattices, symmetry elements, etc. There is lots here to choose from -- I doubt that anyone will want to use all of the images. Studying plane groups is a good way to introduce crystal systems, point groups, lattices, symmetry operators, etc. All is in 2-D, but it is easy to tell students that the principles are the same in 3-D. For those who like to make changes, the PDF document was created from individual EPS files. This means that the files can be opened in Adobe Illustrator, Corel Draw, etc., and modified to fit your own needs.