Tracy Phelps
SLM 521
Drop In # 1
Background from site:
“A Platonic solid is a polyhedron whose faces are identical regular polygons. The ancient Greeks were able to show that there are exactly five such Platonic solids. This virtual manipulative allows you to display, rotate, and resize Platonic solids. It also allows you to select vertices, edges, and faces, and show that the number of vertices minus the number of edges plus the number of faces is equal to 2 (Euler’s formula).”Using the National Library of Virtual Manipulatives site on platonic solids, complete the table below.
1. Go to this site:
http://nlvm.usu.edu/en/nav/frames_asid_128_g_2_t_3.html?open=instructions2. Using the directions on the screen/ below, rotate the shape to count the number of edges, faces, and vertices of each shape in the table.
To rotate: click and hold down the left mouse button, drag the mouse anywhere in the box and the solid will rotate.
To count the faces: Click one of the color buttons. Hold the Shift key down on your keyboard and click on a face of the Platonic solid. The face will be painted the selected color. Count the faces of the Platonic solid.
To count the edges: Hold the Shift key down on your keyboard and click on an edge or vertex.
3. While counting, complete the table below.
|
Name of Shape |
Faces |
Edges |
Vertices |
|
Tetrahedron |
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|
Cube |
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|
Octahedron |
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|
Dodecahedron |
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|
Icosahedron |
4a. For each shape, use the formula V (vertices) - E (edges) + F (faces) to find a similarity between these shapes. Show your work in the box.
|
Name of Shape |
Work |
Answer |
|
Tetrahedron |
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|
Cube |
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|
Octahedron |
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|
Dodecahedron |
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|
Icosahedron |
4b. What similarity did you find after using the formula?
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5. Do you think this rule works for other three-dimensional shapes? Why or why not?
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