1 Geometry Section 6-1C Exploring Polyhedrons Pg. 409 Quiz Tomorrow

2 Pg. 410 Definitions: Polyhedron: Three-dimensional figures whose faces are triangles, rectangles and other polygons. Remember – “names” have letters ABCDE, “classifications” are the specific names of the shape.

3 The polyhedron shown is a cube with a corner cut off. a. Name the triangular face of the polyhedron. b. Name the face that includes L, M and Q as vertices. Pg. 410 Try It: c. Find the number of faces, vertices and edges of the polyhedron. RST MLQRT Faces - 7Vertices - 10Edges - 15

4 Pg. 410 Polygons (2-D) are classified by the number of sides they have. Polyhedrons (3-D) are classified by the number of faces they have. 4 faces – tetrahedron 5 faces – pentahedron 6 faces – hexahedron 8 faces – octahedron 12 faces – dodecahedron 20 faces - icosahedron

5 Pg. 411 Explore # of faces (F) # of vertices (V) # of edges (E) a. b. c. d. e. Find the number of faces, vertices and edges in each polyhedron. Can you see the relationship between these numbers? Euler’s Formula F + V – E = 2 or F + V = E + 2

6 1. Name the faces of the polyhedron. #1-4 Pg. 412 Exercises: DEF, ABEF, BCDE, ACDF, ABC 2. Classify the polyhedron pentahedron 3. Find the number of faces, vertices and edges. F - 5V - 6E Verify Euler’s Formula – 9 = 2

7 5. Classify faces 1 and 2 #5-8 Pg. 412 Exercises: 1 - triangle 6. Name the vertices of face 1. P, Q, V 7. Name the sides of face 2. NP, PQ, QR, RS, ST, TU, UM, MN 8. How many faces, vertices and edges? Verify Euler’s Formula F octagon V - 24E – 36 = = 36

8 Homework: Practice 6-1C Quiz Tomorrow