1. 6-3A
Geometry Section 6-3B Regular Polyhedrons Page 448 If you have your solids, you might like to use them today. Test Friday – Shapes on Friday
On the homework worksheet, #12 is the same as the Example in the book (and the proof we work together in the notes) Change this to #16 in the Exercises. Also, add some grids to the backside to help with #11. 1 1

2. 5 regular polyhedrons – let’s take a look.
A regular polyhedron has:
Congruent edges and faces
Faces that are regular polygons
Pg. 448
An equal number of edges meeting at each vertex
A convex regular polyhedron is one with no “dents”.
5 regular polyhedrons – let’s take a look.

3. Regular Polyhedron: There are only 5 convex regular polyhedrons.
Pg. 448
They were discovered over 2000 years ago and are name the Platonic Solids in honor of the Greek philosopher Plato.

4. Explore: (fill in your chart)
Tetrahedron
The faces are triangles
4 faces
Pg. 449
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: (fill in your chart)
Hexahedron
The faces are squares
Pg. 449
6 faces
8 vertices
12 edges
What is the sum of the measures of the angles that meet at each vertex?
270o

6. Explore: (fill in your chart)
Octahedron
The faces are triangles
Pg. 449
8 faces
6 vertices
12 edges
What is the sum of the measures of the angles that meet at each vertex?
240o

7. Explore: (fill in your chart)
Dodecahedron
The faces are pentagons
Pg. 449
12 faces
20 vertices
30 edges
What is the sum of the measures of the angles that meet at each vertex?
324o

8. Explore: (fill in your chart)
Icosahedron
The faces are triangles
Pg. 449
20 faces
12 vertices
30 edges
What is the sum of the measures of the angles that meet at each vertex?
300o

9. Classify each regular polyhedron.
Exercises:
Classify each regular polyhedron.
#1-5
Pg. 450
1. tetraheadron
2. octahedron
3. hexahedron
4. dodecahedron
5. icosahedron

10. Exercises: octahedron dodecahedron
Name the convex regular polyhedron that has the given set of characteristics.
6. Four equilateral triangles meeting at each vertex.
#6-7
Pg. 450
octahedron
7. Pentagonal faces
dodecahedron

11. Exercises:
If a platonic solid is randomly selected from the 5 possibilities, what is the probability that the solid will have:
3 5
a. triangular faces
#12
Pg. 450
1 5
b. square faces
1 5
c. pentagonal faces

12. Find the sum of the face angles at each vertex of a:
Exercises:
Find the sum of the face angles at each vertex of a:
14. regular octahedron
240o
#14-15
Pg. 450
15. regular dodecahedron
324o

13. Homework: Practice 6-3B Test Friday
Solids due Friday