What Is a Polygon?
Let's start with the basics. A polygon is one of the most fundamental shapes in geometry, and you see them everywhere — from stop signs to floor tiles to honeycomb patterns.
A closed two-dimensional shape made up of straight line segments (called sides) that do not cross each other. Each side meets exactly two other sides at its endpoints (called vertices).
The word polygon comes from Greek: poly means "many" and gon means "angle." So a polygon is literally a shape with many angles!
Key requirements for a shape to be a polygon:
- It must be a closed figure (no gaps)
- It must be made of straight lines only (no curves)
- The sides must not cross each other
- It must be a flat (2D) shape
A circle is not a polygon because it has no straight sides. A shape with sides that cross each other (like a figure-eight) is also not a polygon.
Polygons are named by their number of sides:
| Number of Sides | Name |
|---|---|
| 3 | Triangle |
| 4 | Quadrilateral |
| 5 | Pentagon |
| 6 | Hexagon |
| 7 | Heptagon |
| 8 | Octagon |
| 9 | Nonagon |
| 10 | Decagon |
| 11 | Hendecagon |
| 12 | Dodecagon |
| -gon |
The table above shows the most commonly encountered polygon names. Any polygon can always be described as an "-gon" — for example, a 14-sided polygon is called a 14-gon (or tetradecagon).
Convex vs. Concave Polygons
Not all polygons look the same — one of the most important distinctions is whether a polygon is convex or concave.
A polygon where all interior angles are less than 180°. If you pick any two points inside the polygon and draw a line segment between them, that segment stays entirely inside the shape.
A polygon that has at least one interior angle greater than 180° (a reflex angle, measured on the interior side of the boundary). This creates a "dent" or "cave" in the shape — the boundary curves inward at that vertex. A line segment drawn between two interior points may pass outside the polygon.
Think of the word "concave" — it has the word cave in it. A concave polygon has a "cave" or indent that pushes inward. A convex polygon "puffs out" everywhere, like a fully inflated balloon.
How to tell them apart:
- Convex: All vertices point outward. Every interior angle is less than .
- Concave: At least one vertex points inward (creating a dent). At least one interior angle is greater than .
Diagram: On the left, a convex hexagon with all vertices pointing outward and all interior angles marked as less than 180°. On the right, a concave polygon (arrow shape) with one vertex pointing inward and the reflex interior angle (greater than 180°) clearly marked at the dent.
Quick test: Place a rubber band around the polygon. If the rubber band touches every side, the polygon is convex. If the rubber band "skips over" a dent without touching a side, the polygon is concave.
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