Define Euler's relation between the number of faces, number of edges and number of vertices for various 3-dimensional figures.
Leonhard Euler has defined the relation between the number of faces, number of edges and number of vertices for various 3-dimensional figures is called as Euler's formula. This formula works with shapes called Polyhedron. A Polyhedron is a closed solid shape which has flat faces and straight edges like cube.
According to him
F + V – E = 2
Where F denotes the number of face
V denotes the number of vertices
E denotes the number of edges.
Shape | Faces | Vertices | Edges | F + V – E |
Cube | 6 | 8 | 12 | 2 |
Octahedron | 8 | 6 | 12 | 2 |