What are the 7 types of Crystals

7-types of crystals: 

On the basis of axial length in x,y, z-direction, and interfacial angles between them,unit cell can be classified into seven types which are called Seven Crystal System.

7- Crystal Habits
Axial Length
Interfacial Angles
Cubic
a = b = c        
α = β = γ = 90˚
Tetragonal
a = b c        
α = β = γ =90˚
Orthorhombic(Rhombic)
a ≠ b ≠ c        
α = β = γ =90˚
Monoclinic
a ≠ b ≠ c        
α = γ =90˚ ,  β 90˚
Triclinic
a ≠ b ≠ c        
α β γ 90˚
Hexagonal
a = b ≠ c        
α = β = 90 ˚ , γ =120˚
Rhombohedral
a = b = c        
α = β = γ 90˚

Where a,b,c is the length of x,y and z-axis respectively.

α,β,γ  is the interfacial angle between x-axis and y-axis, y-axis and z-axis, z-axis and x-axis respectively.

Note:

Most symmetric crystal -Cubic Crystal
Most unsymmetric crystal -Triclinic Crystal
To remember this crystal system we have derived a formula and i.e. 
            CUTE OUR MOTHER
CU-Cubic
TE-tetragonal
OUR-Orthorhombic
MO-Monoclinic
T-Triclinic
HE-Hexagonal
R-Rhombohedral

UNIT CELL

What is unit cell? 

The smallest part of the complete space lattice which on repetition again and again in all the possible direction results in the formation of crystal lattice/space lattice is called a unit cell. 

Contribution of a lattice point at a particular position:

location             Contribution
Body center       1
Face center        1/2
Edge center       1/4
Corner               1/8

Classification of the unit cell?

On the basis of the location of the lattice point within the unit cell, there may be two types of unit cells.

1st classification of unit cell

1.Primitive unit cell

In this type of unit cell lattice points are present only at corners.
For example SCC(Simple Cubic Unit Cell)
Lattice points at the corner
Coordination number(Z)=8*1/8=1

2.Non-Primitive unit cell

In this type of unit cell lattice points are present not only at corners but also at some other specific position. For example,
(a)BCC(Body center cubic unit cell)
Coordination number(Z)=Lattice point at corner+Lattice point at the body
                                        =(8*1/8)+1=2
(b)FCC(Face center cubic unit cell)
Coordination number(Z)=Lattice point at all corner+lattice point at each face
                                        =(8*1/8)+(6*1/2)
                                        =1+3=4
Where the coordination number(Z)is the total number of particles or atoms or lattice points per unit cell.

2nd classification of unit cell:

On the basis of axial length in x,y, z-direction, and interfacial angles unit cell can be classified into 7 types which are called seven crystal system or seven crystal habits and these are Cubic, Tetragonal, Orthorhombic(Rhombic), Monoclinic, Triclinic, Hexagonal, Rhombohedral.

For brief understanding about the above seven crystals, follow the link below: