Question

dylan says he has a polyhedron with 8 faces, 7 vertices and 10 edges. dylan has made a mistake, two of his values are correct, state the possible correct number of faces, vertices and edges.

Answer 1

• 5 faces
• 4 vertices
• 13 edges

Explanation:

Given two of three numbers correct, you want to find the correct value for the third number of 8 faces, 7 vertices, and 10 edges.

Euler's formula

The relation between faces, vertices, and edges is ...

F + V = E + 2

The given numbers are off by 3:

8 + 7 = 15 ≠ 12 = 10 + 2

Application

We can decrease the numbers of Faces or Vertices by 3, or we can increase the number of Edges by 3.

The numbers will be correct if we change to ...

• 5 faces, or
• 4 vertices, or
• 13 edges

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