1. What do they all have in common?
Pyramids
What do they all have in common?

2. Pyramids
Definition
A solid object where: • The base is a polygon (a straight-sided flat shape) • The sides are triangles which meet at the top (the apex).

3. What do they all have in common?
Prisms
What do they all have in common?

4. Prisms
Definition
A solid object with two identical ends and flat sides: • The sides are rectangles (or parallelograms)
• The cross section is the same all along its length The shape of the ends give the prism a name, such as "triangular prism"

5. face

6. edge

7. vertex (plural vertices)

8. Fill in the table for each of the pyramids
Solid
Number of Faces
Number of Edges
Number of Vertices
Can you find a predict the results for a heptagonal or octagonal based pyramid? What about an n-agonal based pyramid?

9. Pyramids Fill in the table for each of the pyramids Solid
Number of Faces
Number of Edges
Number of Vertices
Can you find a connection between the Faces, Edges and Vertices?

10. V + F - E = 2. Euler’s Formula for Polyhedra
The formula was discovered by and bears the name of the famous Swiss mathematician Leonhard Euler ( )
It is true for all polyhedra.
(singular – polyhedron)

11. Fill in the table for each of the prisms
Solid
Number of Faces
Number of Edges
Number of Vertices
Can you find a predict the results for a heptagonal or octagonal prism? What about an n-agonal prism?

12. Prisms Fill in the table for each of the prisms Solid Number of Faces
Number of Edges
Number of Vertices
Verify that Euler’s formula also works for the prisms in this table

13. Other Polyhedra Fill in the table for each of these platonic solids
Number of Faces
Number of Edges
Number of Vertices
Octahedron
Dodecahedron
Icosahedron
How can you use Euler’s formula to fill in this table?

14. Why are there only 5 platonic solids?