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