Problem #6
Note: In this problem, all distances are to be measured
along the surface of the figure.
For each of the regular polyhedra (see the animated gif's below), answer
the following questions given that the length of an edge is 1 unit:
- What is the furthest apart two points on the surface can be?
- What is the furthest apart three points can be?
- What is the furthest apart four points can be?
Specifically, we want the minimum distance between the points to be as
large as possible.
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| tetrahedron |
octahedron |
cube |
icosahedron |
dodecahedron |
(GIF's © 1998,
R. Mäder)