Seven Crystalline Structures 
definition 

Triclinic  requires either a center
or only translational symmetry. Angles are all different 

Monoclinic  1 two fold axis of
rotation or 1 mirror plane 

Orthorhombic 
requires either 3 two fold axis of rotation or 1 two fold axis of rotation
and two mirror planes. 

Hexagonal
 6 part symmetry
(one 6 fold); all sides are not equal; 60E
angles 