Verifying Euler's Relation for 3-D Figures with Flat Faces

 

Polyhedron is a closed solid shape which has flat faces and straight edges.

Example: Cube

Image result for CUBE

Euler's formula deals with shapes called Polyhedra. 

Euler's formula states that for Polyhedra that follow certain rules, like the shape must not have any holes, and that it must not intersect itself.

F+V-E=2

Where F= Number of faces, V= Number of vertices (Corners), E=Number of edges

Let us check that this works for the Tetrahedron (triangle based pyramid) and the cube.

Image result for CUBE

Shape

Faces

Vertices

Edges

F+V-E

Tetrahedron

4

4

6

4+4-6=2

Cube

6

8

12

6+8-12=2