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What is an octagon?

What is an octagon? Here are some definitions.

Noun
  1. (geometry) A polygon with eight sides and eight angles.
  2. (martial arts, usually capitalized) The arena for mixed martial arts, particularly as trademarked by the UFC.
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Examples
Each vertex triangle of the octagon is a vertex triangle of one such parallelogram.
Only a handful of gunsmiths have the ability to cut a tapered octagon barrel.
If you think of an octagon as a square with its corners cut off, you'll realize how simple the shape truly is.
Goodbye to the quaint packaging, goodbye to the fruit-and-nut delight, and so-long to the vanilla octagon.
The octagon is formed by a kind of train-track motif that jogs around a flower-blossom design.
The octagon is then placed on the white stand, where it is fixed into a star formation with the help of a metal bracket.

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