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Answer:

A polyhedron with 6 faces and 8 vertices has 12 edges.

Step-by-step explanation:

Euler Formula is given in the problem:

  • F + V = E + 2  

We are told that the polyhedron has 6 faces (F = 6) and 8 vertices (V = 8). The only unknown variable in Euler's Formula now is E = number of edges.

Substitute the known variables into the formula and solve for E.

  • 6 + 8 = E + 2
  • 14 = E + 2
  • 12 = E
  • E = 12

A polyhedron with 6 faces and 8 vertices has 12 edges.
Given:

Number of faces = 6

Number of vertices = 8

Formula used:

Euler's formula:

F + V - E = 2

F = Number of Faces of Polyhedron

V = Number of Vertices of Polyhedron

E = Number of Edges of Polyhedron

Calculations:

Let the polyhedron have E edges,

6 + 8 - E = 2

14 - E = 2

E = 14 - 2

E = 12

Therefore:

The Polyhedron has 12 edges

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