Lecture 9 • Autumn 2026

3D Crystallography &
Bravais Lattices

Named after Auguste Bravais (1848), discover how systematically extruding the 17 unique 2D plane groups into the third dimension enforces strict geometric constraints, yielding exactly 14 unique 3D lattice types.

Interactive Extrusion Engine

Deriving the 14 Bravais Lattices

Select any of the 17 plane groups below. Watch how symmetry elements (like mirrors and rotation axes) form infinite 3D boundaries. To prevent breaking these symmetries, the extrusion vector ($c$) must snap to specific alignments, revealing the 14 Bravais Lattices.

The 17 Plane Groups

Select to extrude

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Status
Basal Plane (y=0)
Extruded Planes
Extrusion Vector Paths
3D Unit Cell (Conventional)
Mirror Plane
Glide Plane
Rotation Axis
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