# The 14 Bravais Lattices

**(Drag with mouse over each object to rotate)**

**Cubic Lattices:**

**Tetragonal Lattices:**

**Orthorhombic Lattices:**

**Hexagonal Lattices:**

**Trigonal Lattices:**

**Monoclinic Lattices:**

**Triclinic Lattices:**

#### Self-test Questions:

- Which of these cells are
*primitive cells?*

- How many lattice points per cell?

- Can you see any
*n*-fold rotation axes, where
*n* =
- 3
- 4
- 2

(Look for them by rotating the object until an *n*-fold axis
is perpendicular to the screen: do you see the *n*-fold symmetry
now?)
How many rotation axes are there of each type? What are their Miller
indices?

- How about mirror planes?

- View each of the cubic cells along a <111> direction. What is
the rotational symmetry about this axis? Which structure (sc, fcc,
bcc) is the most/least densely packed?

- Why is there no such lattice type as, e.g., ``face-centered (
*F*)
tetragonal''?
``Base-centered (*C*) tetragonal''?

- Can you see how to represent a primitive trigonal lattice in terms of
the hexagonal conventional cell (i.e., a hexagonal lattice with an
*n*-atom basis)?
What is the value of *n*?

© 1999 R. J. Hauenstein