The 14 Bravais Lattices

Structural Reference Guide

In 3D space, there are exactly 14 unique ways to arrange points in a repeating lattice such that each point has an identical environment. These are the 14 Bravais Lattices, categorized into 7 Crystal Systems.

System	Axial Lengths	Interaxial Angles	Lattice Types
Cubic	a = b = c	α = β = γ = 90°	P, I, F
Tetragonal	a = b ≠ c	α = β = γ = 90°	P, I
Orthorhombic	a ≠ b ≠ c	α = β = γ = 90°	P, I, F, C
Hexagonal	a = b ≠ c	α = β = 90°, γ = 120°	P
Rhombohedral	a = b = c	α = β = γ ≠ 90°	P
Monoclinic	a ≠ b ≠ c	α = γ = 90°, β ≠ 90°	P, C
Triclinic	a ≠ b ≠ c	α ≠ β ≠ γ ≠ 90°	P

P

Primitive (Simple)

I

Body-Centered

F

Face-Centered

C

Base-Centered

Bravais Lattices Reference Sheet

Bravais Lattices Reference Sheet