a polygon
/ POL-ee-gon /
Think of a fence built from straight planks, each joined end to end, that finally closes back on itself with no gap and no overlap — the boundary it traces is a polygon. A triangle, a square, the outline of a stop sign, and the pentagon of a soccer-ball patch are all polygons. The word comes from Greek: poly (many) and gonia (angle), so a polygon is literally a 'many-angled' figure.
Precisely, a polygon is a closed figure in a plane made of finitely many straight line segments, called its sides or edges, joined so that each endpoint, called a vertex, belongs to exactly two sides, and no two sides cross. A polygon with n sides has exactly n vertices and is called an n-gon: 3 sides a triangle, 4 a quadrilateral, 5 a pentagon, 6 a hexagon, 8 an octagon, and so on. The sides enclose a region — the polygon's interior — though in this field we study the figure's angles, sides, and diagonals rather than the area of that region, which belongs to Measurement.
A common slip is to call a curved outline, like a circle or an ellipse, a polygon — it is not, because its boundary is not made of straight segments. Equally, a figure whose sides cross itself (a 'star' drawn in one stroke, like a pentagram) is a self-intersecting or star polygon, a separate family; the plain word 'polygon' in school geometry means the simple, non-crossing kind. We also require the sides to be genuine segments, so two adjacent sides may not lie on the same straight line (that would erase a vertex).
A traffic stop sign has 8 straight equal edges meeting at 8 corners, so it is an octagon — an 8-gon. A standard pencil's cross-section is a hexagon (6 sides). Each is a simple, non-crossing polygon.
Naming a polygon by counting its sides (= its vertices).
A circle is not a polygon — its boundary is curved, not made of straight segments. And a many-sided regular polygon only approaches a circle as the side count grows without bound; it never becomes one.