Question

How many faces does a polyhedron have if ithas 8 vertices and 12 edges?

Answer 1

6 faces

Explanation:

The relationship between the number of faces, edges, and vertices in a polyhedron is represented by Euler's Formula:

`F+V-E=2,where\begin{cases}{{\text{F = number of faces}}} \\ {\text{V = number of vertices}} \\ {\text{E = number of edges}}\end{cases}`

Given a polyhedron in which:

• V=8

,

• E=12

Substitute into the formula above:

`\begin{gathered} F+8-12=2 \\ F-4=2 \\ F=2+4 \\ F=6 \end{gathered}`

A polyhedron with 8 vertices and 12 edges will have 6 faces.