Polyhedra and Prisms

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.

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

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.

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?

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.

Euler’s Theorem

• F + V = E + 2 • F = the number of faces• V = the number of vertices• E = the number of edges

Platonic Solids

Tetrahedron

Octahedron

Dodecahedron

Icosahedron