EULER'S FORMULA
F + C = E + 2
F   =   number of faces
C   =  number of corners (vertices)
E   =  number of edges

 

Tetrahedron

F   =   4
C   =  4
E   =  6

4 + 4  =  6 + 2


 

Cube

F   =   6
C   =  8
E   =  12

6 + 8  =  12 + 2


 

Octahedron

F   =   8
C   =  6
E   =  12

8 + 6  =  12 + 2


 

Dodecahedron

F   =   12
C   =  20
E   =  30

12 + 20  =  30 + 2


 

Icosahedron

F   =   20
C   = 12
E   =  30

20 + 12  =  30 + 2