If a convex polyhedron has 18 edges and 12 vertices, then how many faces does it have?

Question

Parker

Mathematics

24 December, 02:26

If a convex polyhedron has 18 edges and 12 vertices, then how many faces does it have?

+2

Answers (1)

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Summer Case · Answer 1

Use Euler's characteristic.

V - E + F = 2

Now substitute and solve for F.

V - E + F = 2

12 - 18 + F = 2

-6 + F = 2

F = 8

Therefore the polyhedron has 8 faces.