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According to Wikipedia:

"Refraction is the change in direction of a wave due to a change in its speed."

So your question could also be "Why is control of the light wave through a diamond stone important to a diamond cutter?"

To maximize the brilliance/ shine/ flash/ fire of a diamond cut, a stone cutter must craft the stone facets in a geometric pattern that honours diamond's natural high refraction index (2.4), so that light can 'bounce' into, within and out of the stone to the highest degree possible.

Read more, below.

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Q: Why is refraction important to diamond cutters?
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