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Why do fullerene molecules utilise pentagons and hexagons?

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Why do fullerene molecules utilise pentagons and hexagons?

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We use pentagons and hexagons to try to draw a structure for the molecule, but the reality is that the atoms exist in certain positions just like there are lines on a football field. We wouldn’t ask the significance of the rectangles formed on the football grid. Answering the question of why the atoms are arranged the way they are, might one say that they are of maximum stability.

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