Question

Verify Euler's formula for

(a) Tetrahedron

(b) Hexagonal prism

Answer 1

Euler's formula for polyhedron is:

• V - E + F = 2
• where V- vertex, E- edge, F- face

As per the above formula the relationship between the vertexes, edges and faces is same for any polyhedron.

Lets confirm, have a look at the picture

(a) Tetrahedron, count each element:

• V = 5, E = 8, F = 5

Verify

• 5 - 8 + 5 = 10 - 8 = 2 - correct

(b) Hexagonal prism, count each element:

• V = 12, E = 18, F = 8

Verify

• 12 - 18 + 8 = 20 - 18 = 2 - correct