Question

please answer the question ​

Answer 1

Euler's Formula

For any polyhedron that doesn't intersect itself, the

Number of Faces

plus the Number of Vertices (corner points)

minus the Number of Edges

always equals 2

This can be written: F + V − E = 2

hexahedron

Try it on the cube:

A cube has 6 Faces, 8 Vertices, and 12 Edges,

so:

6 + 8 − 12 = 2

Example With Platonic Solids

Let's try with the 5 Platonic Solids:

Name Faces Vertices Edges F+V-E

Tetrahedron Tetrahedron 4 4 6 2

Cube Cube 6 8 12 2

Octahedron Octahedron 8 6 12 2

Dodecahedron Dodecahedron 12 20 30 2

Icosahedron Icosahedron 20 12 30 2

(In fact Euler's Formula can be used to prove there are only 5 Platonic Solids)

Why always 2?

Imagine taking the cube and adding an edge

(from corner to corner of one face).

We get an extra edge, plus an extra face:

7 + 8 − 13 = 2

its the answer....