Crystal Explorer - Interactive Crystallography

Explore the seven crystal systems and the 14 Bravais lattices. Visualise unit cells, crystal directions, and Miller planes, and investigate their geometric relationships interactively.

Bravais Lattice

Number of cells

Cell parameters

Cell lengths (nm)
a: b: c:

Angles (degrees)
alpha: beta: gamma:

Directions

Direction 1 u: v: t: w: Visible

Direction 2 u: v: t: w: Visible

Planes

Plane 1 h: k: i: l: Visible

Plane 2 h: k: i: l: Visible

Explore the 32 crystallographic point groups. Enter the fractional coordinates of a general point to display the symmetry-equivalent points together with the corresponding symmetry elements.

Point group

General point x: y: z:

Explore all 230 crystallographic space groups. Display the symmetry elements and equivalent positions generated from Hermann–Mauguin or Hall symbols.

Space group

General point x: y: z:

About

This website was created to make crystallography more accessible through interactive visualisation and computation.

It brings together many of the core concepts used in crystallography—including crystal systems, Bravais lattices, point groups, space groups, Miller planes, crystal directions, and symmetry operations—into a single browser-based application. Rather than simply presenting tables of data, the site allows these concepts to be explored visually with interactive 3D models.

The application is designed for students learning crystallography, educators looking for teaching resources, and anyone with an interest in crystal symmetry. All calculations are performed directly in your browser, requiring no software installation.

About the Project

This project was developed as an independent educational resource using modern web technologies. All graphics are rendered interactively in the browser, making the application available on desktop and mobile devices without requiring additional software.

Suggestions, comments, and reports of any errors are always welcome and will help improve the site for future users.

References

Giacovazzo, C. (Ed.). Fundamentals of Crystallography. International Union of Crystallography Texts on Crystallography. Oxford University Press, 1992.
Grosse-Kunstleve, R. W. (1999). "Algorithms for deriving crystallographic space-group information." Acta Crystallographica Section A: Foundations of Crystallography, 55(2), 383–395.
Grosse-Kunstleve, R. W., & Adams, P. D. (2002). "Algorithms for deriving crystallographic space-group information. II. Treatment of special positions." Acta Crystallographica Section A: Foundations of Crystallography, 58(1), 60–65.

Align view:

Rotate the model by dragging with the left mouse button.
Use the mouse wheel to zoom in and out.