Mathematical Definition of a Primitive Cell

[ehrenfest]

[SOLVED] primitive cell

Homework Statement

http://en.wikipedia.org/wiki/Primitive_cell
Could someone give me a mathematically rigorous of a primitive cell? I have read like 4 different definitions and none of them seem mathematically rigorous.
I think Wikipedia's definition is particularly ambiguous: "a minimum cell corresponding to a single lattice point" ?
In what sense is minimum being used? In what sense is cell being used?

EDIT: this should probably be in the Advanced Physics section but I cannot delete it or move it

Homework Equations

The Attempt at a Solution

 

[ehrenfest]

Someone PLEASE HELP this problem is driving me insane.

In the picture in the Crystal Structure section of http://en.wikipedia.org/wiki/NaCl, what is the primitive cell AND WHY?

 

[ehrenfest]

I think I understand now. Go to http://www.neutron.anl.gov/hyper-physics/bravais.html .

The primitive cell of the cubic face-centered structure of the NaCl lattice IS NOT THE CUBE. The cube is the CONVENTIONAL cell for the primitive face-centered cubic structure (e.g. NaCl) but IT CANNOT BE THE PRIMITIVE CELL BECAUSE IT CONTAINS 4 LATTICE POINTS WHICH IS MORE THAN 1.

The primitive cell of the the fcc crystal is actually a rhombohedron.

 

[malawi_glenn]

You got the idea :) Crystal structure is quite hard in the beginning, many new things to learn.