Geometry
Platonic Solids
Information:
A regular solid is made of only one
type of regular polygon. Over 2000 years
ago, the Greek mathematician Euclid proved that only five regular solids, called
the Platonic solids, are possible. A
regular polyhedron is a solid figure whose faces are congruent regular
polygons, with the same number of polygons at each vertex. The five Platonic solids are as follows:
Tetrahedron 4 triangle
Cube 6 square
Octahedron 8 triangle
Dodecahedron 12 pentagon
Icosahedron 20 triangle
Assignment:
1. You will make all five of the Platonic
Solids. You have some choice as to how
you make them. Construct the solids so
that the maximum length of any side of a solid is 6 inches. Some suggestions
for materials are cardstock, old greeting cards, straws and tissue paper,
toothpicks and gumdrops, or anything else you can think of. You may also use circle/inscribed polygon
method shown in class with cardstock or old greeting cards
2. You will make a table listing the number of
faces, vertices, and edges for each of the five solids. Use your Platonic Solids to create and fill in
the table. Once you are done, look for a relationship between the number of edges of each solid. Find a relationship between
the Edges, Vertices, and Faces. This relationship is called Euler's
Formula (pronounced Oiler). Include
this information in your summary paragraph.
|
|
Faces |
Vertices |
Edges |
|
Tetrahedron |
|
|
|
|
Hexahedron (Cube) |
|
|
|
|
Octahedron |
|
|
|
|
Dodecahedron |
|
|
|
|
Icosahedron |
|
|
|
3. You will hang all of your Platonic Solids on
a mobile. Your mobile can be made out of
any material (wire, dowel rods, straws, etc.).
It must be ready to hang when you bring it in to the classroom. It must have a minimum of two tiers. All tiers must be balanced.
4. Summary Paragraph
You will write a paragraph summarizing
this project. This should include three
to four sentences reflecting you opinion about the project, what you learned,
what you do differently, suggestions for future students, etc. You must also include the chart from item #2
and your ideas about Euler’s Formula.
Discuss how you arrived at this formula.
Assessment: (50 pts)
You will be graded
on:
5 solids 20
accurately and neatly made 4
pts each
Chart and formula 10
mobile 10
ready to hang 2
pts
two tiers 3
pts
balanced 5
pts
Summary 10
Total 50