Math 103 Activity
1. Complete the following table with the appropriate numbers.
Polyhedron |
# of vertices V |
# of edges E |
# of faces F |
# of edges on a face: N |
# of edges meeting at a vertex: M |
tetrahedron |
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cube |
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octahedron |
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dodecahedron |
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icosahedron |
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2. Notice that the cube and the octahedron have the same number of edges. Describe two other ways in which the features of these polyhedra can be related.
What can you say about the relation between the features of the dodecahedron and the icosahedron?
3. Using the table in activity 1, complete the following table:
Polyhedron |
F times N |
V times M |
E |
tetrahedron |
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cube |
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octahedron |
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dodecahedron |
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icosahedron |
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What relation do you see between F times N, V times M, and E?
Write a brief explanation for this relation.
[Hint: How many vertices are on an edge? How many polygons meet on an edge?]