Crystal Systems

Crystal System	Bravais Type(s)	External Minimum Symmetry	Unit Cell Properties
Triclinc	P	None	a, b, c, al, be, ga,
Monoclinic	P, C	One 2-fold axis, parallel b (b unique)	a, b, c, 90, be, 90
Orthorhombic	P, I, F	Three perpendicular 2-folds	a, b, c, 90, 90, 90
Tetragonal	P, I	One 4-fold axis, parallel c	a, a, c, 90, 90, 90
Trigonal	P, R	One 3-fold axis	a, a, c, 90, 90, 120
Hexagonal	P	One 6-fold axis	a, a, c, 90, 90, 120
Cubic	P, F, I	Four 3-folds along space diagonal	a, a, ,a, 90, 90, 90

Notes :

Angles alpha, beta , gamma are abbreviated al, be, ga
Systems right handed (thumb is a, index b, middle finger c)
Rhombohedral (a, a, a, al, al, al)can be indexed with hexagonal axes (see drawings of Bravais lattices)
gamma is between lattice vectors a and b
beta is between lattice vectors a and c
I is body centered, from german ' INNENZENTRIERT '
C is the face/plane spanned by lattice vectors a and b.