1. Exploring Solids

2. What is a Polyhedron? Polyhedrons Non-Polyhedrons

3. Do you notice a difference? Polyhedrons Non-Polyhedrons

4. Polyhedrons / A solid that is bounded by polygons that enclose a single region of space / There are two main types of solids: Prisms andPyramids / A solid that is bounded by polygons that enclose a single region of space / There are two main types of solids: Prisms andPyramids

5. Parts of a Polyhedron

6. Face / The polygons that make up the sides of a polyhedron

7. Edge / A line segment formed by the intersection of 2 faces

8. Vertex / A point where 3 or more edges meet

9. Name the Polyhedron and find the number of Faces, Vertices, and Edges a. b.c.

10. a. b.c. F = 5 V = 5 E = 8 F = 5 V = 6 E = 9 F = 8 V = 12 E = 18

11. a. b.c. F = 5 V = 5 E = 8 F = 5 V = 6 E = 9 F = 8 V = 12 E = 18 Does anybody see a pattern?

12. Euler’s Theorem F + V = E + 2

13. Euler’s Theorem F + V = E + 2 Example:

14. Euler’s Theorem F + V = E + 2 Example: F = 6, V = 8, E = 12

15. Euler’s Theorem F + V = E + 2 Example: F = 6, V = 8, E = 12 6 + 8 = 12 +2

16. Euler’s Theorem F + V = E + 2 Example: F = 6, V = 8, E = 12 6 + 8 = 12 +2 14 = 14

17. Example: Use Euler’s Theorem to find the value of n Faces: 5 Vertices: n Edges: 8

18. Example: Use Euler’s Theorem to find the value of n Faces: 5 Vertices: n Edges: 8 F + V = E + 2 5 + n = 8 + 2 5 + n = 10 n = 5 link http://www.youtube.com/watch? v=v1Dcc3ZmuuQ