A polygon is a closed 2D shape with straight sides. Polygons are named using Greek number prefixes combined with the suffix "-gon" (meaning "angle"). For example, penta- (5) + -gon = pentagon. For polygons with 13+ sides, the naming typically uses combined Greek prefixes (e.g., triskaideka- for 13 → triskaidecagon). In practice, polygons with more than 12 sides are often simply called "n-gons" (e.g., 17-gon, 42-gon).

A 3-sided polygon is called a Triangle (also known as a Trigon). It is the simplest polygon possible in Euclidean geometry, with an interior angle sum of 180° (60° per angle for a regular triangle / equilateral triangle). Triangles are the only polygons that are always rigid and cannot be deformed without changing side lengths.

A Decagon has exactly 10 sides and 10 angles. The name comes from the Greek deka- meaning "ten." A regular decagon has interior angles summing to 1,440°, with each interior angle measuring 144°. Decagons appear in architecture, coin designs, and some modern building layouts.

A 7-sided polygon is called a Heptagon (sometimes referred to as a Septagon, though "heptagon" is the preferred Greek-derived term). A regular heptagon has interior angles summing to 900°, with each interior angle measuring approximately 128.57°. Unlike the hexagon, a regular heptagon cannot be constructed with just a compass and straightedge.

The sum of interior angles of an n-sided polygon is calculated using the formula: (n − 2) × 180°. For a regular polygon, each interior angle equals (n − 2) × 180° / n. For example, an octagon (8 sides) has interior angles summing to (8−2)×180° = 1,080°, with each angle measuring 135°.

Polygons with more than 20 sides are typically referred to using the "n-gon" notation (e.g., 25-gon, 60-gon, 100-gon). While formal Greek-based names exist (like icosipentagon for 25 or hexacontagon for 60), these are rarely used in practice due to their complexity. Notable exceptions include the Hectogon (100 sides), Chiliagon (1,000 sides), and Myriagon (10,000 sides). As the number of sides increases, the polygon increasingly resembles a circle.

A 12-sided polygon is called a Dodecagon (from Greek dodeka- meaning "twelve"). A regular dodecagon has interior angles of 150° each, summing to 1,800°. Dodecagons appear in various coin designs (such as the British £1 coin), architectural elements, and in the design of some stop signs in certain countries. The dodecagon is also notable because it can tile the plane when combined with other polygons in specific patterns.

In standard Euclidean plane geometry, a polygon must have at least 3 sides. A Monogon (1 side) would be a single line segment with one vertex — not a closed shape. A Digon (2 sides) would consist of two line segments sharing two vertices, which is degenerate in flat geometry. However, digons do exist in spherical geometry, where the sides are arcs of great circles. For practical purposes, the minimum number of sides for a polygon is 3 (the triangle).