## Real World - Viewing Crystals

Contents || Polyhedra in the Classroom || Suzanne's Math Lessons

[Crystallography]   [Crystal Systems]   [Paper Nets]

Crystallography is a relatively new science. Rene-Just Hauy, who lived in the late 1700s to early 1800s, helped to make crystallography a mathematically exact science by classifying crystals with certain geometric shapes. Christian Westfeld (1746-1823) defined the concept of the unit cell. Christian Weiss (1780-1856) divided crystals into the different crystal systems that are used for classification today.

Crystals form when changing temperatures beneath the earth's surface first melt a mass of molecules and atoms, then cool them slowly. As they cool, the atoms arrange themselves in symmetrical lattices.

Simple molecular structure is the basis of a crystal's form. Crystals take shape according to the way in which their atoms combine. These atoms create regular geometric patterns because they always align themselves in the same way at a given temperature.

A crystal, like a pattern, must have a shape that could extend or repeat itself in all directions indefinitely. That is why the faces of a crystal can only have certain shapes; they could not have anything but the symmetries in the patterns.

From The Ascent of Man by Jacob Bronowski, p. 176.
(This explanation should make you think of regular tessellations. What shapes can be regularly tessellated?)

Scientists have noted that nearly all crystals with the same makeup also have the same shape. All crystals can be classified as one of seven crystal systems.

### Links to Crystal Information on the Web

1. Crystallography Online
Provides extensive coverage of current and internet-based information concerning crystallography and of interest to crystallographers. It is maintained by the International Union of Crystallography.

2. Crystallography Open Database (COD)
The COD, once finalized, will be a keyword-searchable Web server of crystal structure atomic coordinates, preserving the data after publication as well as unpublished data.

3. Crystallography Wikipedia

4. Loes Modderman Microscopic Science-Art
A collection of different and very small crystals, pictured through the microscope.

5. Mineralogy Database
Information on mineralogy including crystallography by David Barthelmy.

6. Minerals, Crystals and Their Systems
This is an introductory listing of definitions and nomenclature concerning gem materials by Charles Lewton-Brain.

7. Surface Explorer
Start using this by going to help in the lower right corner of the screen. Information for the different settings is clearly explained.