1. Polyhedra and Prisms

2. Definitions
A polyhedron is a solid, bounded by polygons (called faces), that enclose a (single) volume, or region of space.
An edge is a line formed by the intersection of 2 faces.
A vertex is a point where 3 or more edges come together.

3. Cylinders, spheres and cones are not polyhedra. Why not?

4. Prisms and Pyramids
A prism has 2 bases that are congruent, and are in parallel planes.
A pyramid has one base that is a polygon.

5. Regular Polyhedra
A Polyhedron is a regular polyhedron if all of its faces are congruent, regular polygons.
A die would be an example.
Would a soccer ball be one, assuming the polygons were planes?

6. Convex Polyhedra
A polyhedron is convex if any 2 points on its surface can be connected by a line segment within or on the surface of the polyhedron.
If a polyhedron does not meet the criteria for being convex, then it would be concave.

7. Euler’s Theorem F + V = E + 2 F = the number of faces
V = the number of vertices
E = the number of edges

8. Platonic Solids

9. Tetrahedron

10. Octahedron

11. Dodecahedron

12. Icosahedron