1. Space Figures and Cross Sections

2. Polyhedra A polyhedron is a three- dimensional figure whose surfaces are polygons. Each polygon is a face of the polyhedron. An edge is a segment that is formed by the intersection of two faces. A vertex is a point where three or more edges intersect. A regular polyhedron is one where all the faces are congruent regular polygons.

3. Identifying Vertices, Edges, and Faces  How many vertices, edges, and faces are in each polyhedron?

4. Cross Sections A cross section is the intersection of a solid and a plane.  What is the cross section formed by the plane and the solid?

5. Space Figures and Cross Sections Lesson 11-1 Notes 11-1 Euler is pronounced “Oiler.” Reading Math

6. Use Euler’s Formula to find the number of edges on a solid with 6 faces and 8 vertices. F + V = E + 2Euler’s Formula 6 + 8 = E + 2Substitute the number of faces and vertices. 12 = ESimplify. A solid with 6 faces and 8 vertices has 12 edges. Space Figures and Cross Sections Lesson 11-1 Quick Check Additional Examples 11-1 Using Euler’s Formula

7. Use Euler’s Formula to solve. 2. A polyhedron with 12 vertices and 30 edges has how many faces?

8. Using Euler’s Formula How many vertices, edges, and faces does the polyhedron have? Use your results to verify Euler’s Formula. F = 8 V = 12 E = 18 F + V = E + 2 8 + 12 = 18 + 2 20 = 20

9. Example For each, find the missing number