It was named after a pentagon, it wasn't the 'Pentagon' that
named the 'pentagon'.
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Hexagon
* * * * *
A pentagon
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pentagon A pentagon.
A 5-sided figure is called a pentagon. pentagon A five sided
figure is called a pentagon
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They are both the same. Pentagon is just a shorter way of saying
the pentagon building. As for if you meant the shape pentagon, it
is called the pentagon because it's shape is a pentagon.