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In a Carbon-60 fullerene, do the edges ALL have the same lengths? (given that this fullerene has both pentagons and hexagons).

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The pentagons and hexagons are all regular so yes
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Geometrically the shape of C-60 fullerene is a truncated icosahedron. It's formed by starting with an icosahedron and slicing off each of the 12 vertices, leaving a pentagonal stump. The truncated icosahedron has two kinds of edges: pentagon-hexagon and hexagon-hexagon. Depending on where you make the cuts, one kind of edge can be longer than the other, or they can be the same length. in C-60 fullerene they are the same length.

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