Leonhard Euler, a Swiss mathematician, discovered a relationship among the numbers of faces, vertices, and edges of any polyhedron. The result is known as Euler's Formula.
The sum of the number of faces (F) and vertices (V) of a polyhedron is two more than the number of its edges (E).
How many vertices, edges, and faces does the polyhedron below have? Use your results to verify Euler's Formula.
How do you verify Euler's Formula?
Find the number of faces, vertices, and edges. Then substitute the values into Euler's Formula to make sure that the equation is true.
Think | Write |
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Count the number of faces. |
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Count the number of vertices. |
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Count the number of edges. |
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Substitute the values into Euler's Formula. |
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faces:
edges: 30
vertices: 20
faces: 20
edges:
vertices: 12