12.1

1. 12.1 Exploring Solids

2. Polyhedron: • Three dimensional closed figure formed by joining three or more polygons • Example:

3. Which of the following are polyhedrons? No Yes Yes Yes No Yes

4. Face: sides of a polyhedron that enclose a single region of space • Edge: a line segment formed by the intersection of two faces • Vertex: a point where three or more edges meet

5. Example: vertex face edge Faces: 6 Vertices: 8 Edges: 12

6. Identify the number of faces, vertices, and edges for each figure. Faces- 5 Vertices- 6 Edges- 9 Faces- 6 Vertices- 8 Edges- 12 Faces- 7 Vertices- 10 Edges- 15 Faces- 6 Vertices- 8 Edges- 12 Faces- 8 Vertices- 12 Edges- 18 Faces- 6 Vertices- 6 Edges- 10

7. Euler’s Theorem: • The number of faces F, vertices V, and edges E of a polyhedron are related by F + V – 2 = E

8. Use Euler’s Theorem to find the unknown number Faces: Vertices: 16 Edges: 22 Faces: 5 Vertices: Edges: 9 Faces: Vertices: 10 Edges: 15 Faces: 20 Vertices: 12 Edges: 8 7 6 30

9. A polyhedron is regular if all of its faces are congruent regular polygons. • A polyhedron is convex if any two points on its surface can be connected by a segment that lies entirely inside or on the polyhedron. regular convex irregular concave

10. Cross Section: the intersection of the plane and the solid

11. Describe the shape formed by the intersection of the plane and the cube pentagon triangle square