A polyhedron of one hundred faces. But what purpose could such an item serve?

A die of course!

No industry has benefited more from polyhedra research than the dice industry. Pen and paper roleplaying games often require dice other than the standard D6. Thus we have the D4, D6, D8, D12, and D20, all regular polyhedra (the only regular polyhedron in fact). Also, there's the less than regular D10, which is like 2 five-faced pyramids stuck together.
As for the D100, it's useful for dice rolls requiring a percentage. The more common method is to roll 2D10 and multiple one of the die rolls by 10 resulting in a number between 0 and 99.
Nevertheless, some roleplayers just aren't satisfed with this system, and so a D100 is the solution. Using a D100 probably has more to do with the coolness factor rather than any supposed increase in the validity of the roll.

Yes, 100-sided dice do exist, and they take half an hour to stop rolling.

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