Themes of the Day:

• Plane (2D) Symmetry
• Translational Symmetry in 3D
• The 6 Crystal Systems
• Point Symmetry

Plane (Two Dimensional) Symmetry

• Translation in 1 and 2 dimensions
• Plane Lattices and Unit Meshes - The Unit Cell
• Plane Lattices in Everyday Life

Translational Symmetry in 3D

• 5 Plane Lattices Translated into 3D become Space Lattices
• Space Lattices & the Unit Cell
• 14 possible Space Lattices - Bravais Lattices
• crystal axes: lengths a, b, c; angles: alpha, beta, gamma
• Triclinic Bravais lattice
• Monoclinic and Orthorhombic Bravais lattices based on repeating a primitive rectangular unit mesh
• Monoclinic and Orthorhombic Bravais lattices based on repeating a centered rectangular unit mesh
• Hexagonal Bravais lattices
• Tetragonal and Cubic Bravais lattices
• 6 Crystal Systems are inherent in the 14 Bravais lattices

The 6 Crystal Systems

Crystal System	Axis Lengths	Angles
Triclinic	a ≠ b ≠ c	α ≠ β ≠ γ
Monoclinic	a ≠ b ≠ c	α = γ = 90o; β > 90o
Orthorhombic	a ≠ b ≠ c	α = β = γ = 90o
Tetragonal	a = b ≠ c	α = β = γ = 90o
Hexagonal	a = b ≠ c	α = β = 90o; γ = 120o
Isometric (Cubic)	a = b = c	α = β = γ = 90o

Point Symmetry

• Mirror Planes
• Rotational Symmetry
• Center of Symmetry
• Rotoinversion
• Notation - See Table 2.1
• Example: Point Symmetry of a Wooden Block
• 10 2D Point Groups
• 32 Point Groups - combinations of Point Symmetry operations - See Table 2.2

Up Next: Combining Point Symmetry and Translational Symmetry to generate Space Groups