Let \(P\) be a regular centigon (100 sided shape) of side length 1. We draw lines in \(P\) and dissect it completely into a number of rhombuses such that all have side length 1, and any pair of the rhombuses are either disjoint, or share only a vertex, or share a whole side.

How many points are the vertices of all the rhombuses in the resulting diagram?

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**Bonus:** Generalize this for a polygon with \(2n\) sides.

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