Three-Three-Dimensional Dimensional

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Math AllianceMarch 21, 2011

Polyhedrons

• In your group, define the following terms:– Face:– Edge:– Vertex:

• Polyhedron: “poly” – many, “hedron” – side/base• Grab Bag Activity

any of the polygons that make up its boundaries

The set of points where two faces intersect.

A point where 3 or more edges meet.

Polyhedrons?

• Are the following Polyhedrons?

Euler’s Formula

Polyhedron # of Vertices # of Faces Faces + Vertices

Edges

Using the shapes in your crate, complete the following table:

Euler’s Formula

What happens to Euler’s formula when you truncate (cut a corner off) a polyhedron?

Explain your reasoning.

Regular Polyhedrons

• How would you define a regular polyhedron? (Turn and talk.)

• Using the straws and pipe cleaners, which different regular polyhedrons can you create?

Regular Polyhedrons

• There are exactly 5 regular polyhedra:

• How do we know we have found them all?

Tetrahedron

Hexahedron

Octahedron

Dodecahedron

Icosahedron

Homework

-Section 11.4 #’s - 7, 8, 9, 10, 11, 12, 15, 21, 22, 37, 40, 44, 51

• Turn in: 7, 12, 15, 22, 37, 51

Cylinders, Spheres, & Cones