Click on the image. It will open a new window or tab in your browser.The mathematician Leonard Euler discovered a relationship (pattern) between the number of faces, edges, and vertices in any polyhedron.
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Based on what you observed in the previous sections, enter the number of faces, vertices, and edges for each polyhedron into the table. When you see a pattern, click the "I See a Pattern" button.
Source: Euler's Theorem, Learner.org
The pattern that you observe is Euler's Formula:
V – E + F = 2
(V = Vertices, E = Edges, F = Faces)
Example: Given a hexagonal prism, use Euler's Formula to find the number of edges.
Count the total number of sides, include the bases. Interactive button. Assistance may be required. Check Your Answer 8
Use the information found in the chart or count the number of vertices. Interactive button. Assistance may be required. Check Your Answer The number of sides of the base multiplied by two or 6 × 2 = 12.
Use Euler's Formula to verify the number of edges in the hexagonal prism: V – E + F = 2
Substitute the values for the variables by moving the tiles to create the equation.
Simplify and solve for E. E = Interactive button. Assistance may be required. Check Your Answer 18
Example: Given a prism with 18 edges in the base, find the number of vertices and edges.
Click on the blanks to check your answers.
