What is the name for a polygon with eight sides?

An eight-sided polygon is an octagon, built from the Greek okto for eight, the same root behind octopus, octave and October, which was the eighth month before the Roman calendar was reshuffled. In a regular octagon every side is the same length and every interior angle is 135 degrees, and those angles are why octagons cannot tile a flat surface on their own; the gaps left between them are squares, and that combination is a common paving and tiling pattern. The shape is instantly recognisable as the stop sign in many countries, chosen deliberately because its unusual outline is identifiable from behind or when the face is obscured by snow. The general rule for interior angles is worth carrying: for a polygon with n sides they add up to 180 times n minus 2, so for an octagon that is 1080 degrees in total, divided among eight corners to give 135 each.

Cutting the corners off a square is the standard way to construct a regular octagon by hand.