Polyhedra and Prisms

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

Polyhedra and Prisms

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