1

Geometry Section 6-3B Geometry Section 6-3B

Regular PolyhedronsRegular Polyhedrons

Page 448Page 448

If you have your solids, you If you have your solids, you might like to use them today.might like to use them today.Test Friday – Shapes on FridayTest Friday – Shapes on Friday

2

Regular Polyhedrons:Regular Polyhedrons:A regular polyhedron has:

Congruent edges and faces

Faces that are regular polygons

An equal number of edges meeting at each vertexPg.448

5 regular polyhedrons – let’s take a look.

A convex regular polyhedron is one with no “dents”.

3

Regular Polyhedron:Regular Polyhedron:There are only 5 convex regular polyhedrons.

They were discovered over 2000 years ago and are name the Platonic Solids in honor of the Greek philosopher Plato.

Pg.448

4

Explore: Explore: (fill in your chart)(fill in your chart)

Tetrahedron

Pg.449

The faces are triangles

4 faces

4 vertices

6 edges

THINK: If each triangle is regular, what is the measure of each angle? 60o

So what is the sum of the measures of the angles that meet at each vertex? 180o

5

Explore: Explore: (fill in your chart)(fill in your chart)

Hexahedron

Pg.449

The faces are squares

6 faces

8 vertices

12 edges

What is the sum of the measures of the angles that meet at each vertex? 270o

6

Explore: Explore: (fill in your chart)(fill in your chart)

Octahedron

Pg.449

The faces are triangles

8 faces

6 vertices

12 edges

What is the sum of the measures of the angles that meet at each vertex? 240o

7

Explore: Explore: (fill in your chart)(fill in your chart)

Dodecahedron

Pg.449

The faces are pentagons

12 faces

20 vertices

30 edges

What is the sum of the measures of the angles that meet at each vertex? 324o

8

Explore: Explore: (fill in your chart)(fill in your chart)

Icosahedron

Pg.449

The faces are triangles

20 faces

12 vertices

30 edges

What is the sum of the measures of the angles that meet at each vertex? 300o

9

Exercises:Exercises:

#1-5

Pg.450

Classify each regular polyhedron.

1. tetraheadron2. octahedron 3. hexahedron 4. dodecahedron 5. icosahedron

10

Exercises:Exercises:

#6-7

Pg.450

Name the convex regular polyhedron that has the given set of characteristics.

6. Four equilateral triangles meeting at each vertex.

octahedron

dodecahedron

7. Pentagonal faces

11

Exercises:Exercises:

#12

Pg.450

If a platonic solid is randomly selected from the 5 possibilities, what is the probability that the solid

will have:

a. triangular faces 35

b. square faces 15

c. pentagonal faces 15

12

Exercises:Exercises:

#14-15

Pg.450

Find the sum of the face angles at each vertex of a:

14. regular octahedron 240o

15. regular dodecahedron 324o

13

Homework: Practice 6-3B

Test Friday

Solids due Friday