3.2 Crystal Systems, Counting Atoms, Lattice + Basis

Rotational symmetry in 3D

Mirror planes in 3D

High vs low symmetry

Rotation and mirror symmetry

Rotoinversion symmetry 3D

Rotation + mirror plane vs rotoinversion

unique operator combinations:

Example of a point group

3D Unit Cell Dimmensions

7 Crystal Systems that fill 3D Space

Flow chart for determining crystal system

Primitive lattices

Lattice types

The 14 Bravais Lattices

Conventional unit cells, and which types have them?

Bravais lattices vs crystal systems

This is one of those things that feels confusing until you see the hierarchy clearly. The key is:

“primitive, body-centered, face-centered” = lattice types
Bravais lattices = full classification (crystal system + lattice type)

Crystal system: geometry of the unit cell

Unit cell of hexagonal close packed

Unit cell of face centered cubic

Unit cell of body centered cubic

Sharing rules for counting atoms

Theoretical density calculation

Lattice sites

What to put on lattice sites?

Lattice site equivalency

Lattice + basis

Bavais lattices again