# Some Symmetry Operations in Crystallography

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Coordinate transformations are commonly used in crystallography to characterize the crystal symmetry. The four symmetry operations that can occur in three-dimensional geometry are rotation, reflection, inversion, and translation. This Demonstration shows rotation and rotation with inversion (roto-inversion). The original coordinate system (labeled , , ) is colored blue and the new coordinate system (labeled , , ) is colored orange. The black arrow is the axis about which the rotation occurs; the direction of the arrow is controlled with the (theta) and (phi) sliders; is the angle between the black arrow and and is the angle in the - plane between the arrow and the axis, where and (both angles are in radians). Rotation operations are described as "-fold" where refers to the number of steps to complete a full rotation. For example, a fourfold rotation means 4 steps of for a full rotation about the axis.

Contributed by: Robert McIntosh (March 2013)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

detailSectionParagraph## Permanent Citation

"Some Symmetry Operations in Crystallography"

http://demonstrations.wolfram.com/SomeSymmetryOperationsInCrystallography/

Wolfram Demonstrations Project

Published: March 13 2013