Unit Cell 

A UNIT CELL is the smallest unit of volume that contains all of the structural and symmetry information and that by translation can reproduce a pattern in all of space. Structural information the pattern (atoms) plus all surrounding space. Symmetry information mirrors, glides, axes, and inversion centers. Translation motion along a cell edge the length of the cell edge. 

An ASYMMETRIC UNIT is the smallest unit of volume that contains all of the structural information and that by application of the symmetry operations can reproduce the UNIT CELL. Structural information the pattern (atoms) plus all surrounding space. Symmetry information mirrors, glides, axes, and inversion centers. 

The shape of the unit cell is constrained by the collection of symmetry elements which makeup the group. 
Triclinic

Monoclinic 
Orthorhombic

Tetragonal

Hexagonal

Rhombic

Cubic
