They are named for the number of sides and angles their shape posses. For example, an octagon has both eight sides and angles.
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yes they all have special names.
polygons
There are infinitely many polygons so it would be impossible to name them all. For the names of those with a fewer sides see the related link.
These are all names of polygons.
There are an infinite number of different polygons, and some have them have more than one name.