1

Geometry Section 6-1C Geometry Section 6-1C

Exploring PolyhedronsExploring Polyhedrons

Pg. 409Pg. 409

Quiz TomorrowQuiz Tomorrow

2

Pg.410

Definitions: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:Try It:

c. Find the number of faces, vertices and edges of the polyhedron.

RST

MLQRT

Faces - 7 Vertices - 10 Edges - 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 – pentahedron6 faces – hexahedron 8 faces – octahedron12 faces – dodecahedron 20 faces - icosahedron

5

Pg.411

ExploreExplore

# 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?

46875

486

106

61212159

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:Exercises:

DEF, ABEF, BCDE, ACDF, ABC

2. Classify the polyhedron

pentahedron

3. Find the number of faces, vertices and edges.

F - 5 V - 6 E - 9

4. Verify Euler’s Formula

5 + 6 – 9 = 2

7

5. Classify faces 1 and 2

#5-8

Pg.412

Exercises: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 - 14

2 - octagon

V - 24 E - 36 14 + 24 – 36 = 2

14 + 24 + 2 = 36

8

Homework: Practice 6-1CQuiz Tomorrow