A 60 sided polygon is called a hexacontagon.
It's quite acceptable to call it a 60-agon but what is more important is knowing how to work out its properties.
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A 360 sided polygon is known as a Trictohexacontagon. Tricto=300 Hexaconta=60
A five-sided polygon is called a pentagon.
A 39 sided polygon is called a 39-gon.
A thousand-sided polygon is a chiliagon.
hectoctagon is a 108 sided polygon