Question

A convex polyhedron has faces that consist of 6 octagons, 8 hexagons, and 12 squares. The polyhedron has 48 vertices. How many edges does it have?

Euler’s formula: V + F = E + 2

24
26
72
74

Answer 1

Option C is correct.

Explanation:

We are given Euler's Formula,

V + F = E + 2

where V = number of vertex

F = Number of faces

E = Number of Edges

Convex polyhedron has 6 octagons , 8 hexagons and 12 square as faces.

⇒ Number of faces , F = 6 + 8 + 12 = 26

Number of vertices , V = 48

We have to find : Number of edges.

Using Euler's formula,

48 + 26 = E + 2

E = 74 - 2

E = 72

Therefore, Option C is correct.

Answer 2

6 + 8 + 12 = 26 Faces

Edges = Vertices + Faces -2

Edges = 48 + 26 -2

Edges = 72