Polygon

A polygon is a closed two-dimensional figure formed by straight line segments. Each segment is a side, and each meeting point is a vertex.

Classification by number of sides:

• 3: triangle
• 4: quadrilateral (square, rectangle, rhombus, trapezoid, parallelogram)
• 5: pentagon
• 6: hexagon
• 7: heptagon
• 8: octagon
• 10: decagon
• $n$: $n$-gon

A polygon is regular when all sides and all angles are equal (equilateral triangle, square, regular pentagon, ...). A regular hexagon has interior angles of $120°$ and tiles the plane — which is why honeycombs are hexagonal.

Key formulas:

• Sum of interior angles: $(n - 2) \cdot 180°$.
• Each interior angle of a regular $n$-gon: $\frac{(n-2) \cdot 180°}{n}$.
• Sum of exterior angles: always $360°$, regardless of $n$.

A polygon is convex if all interior angles are $< 180°$ (no "dents") and concave otherwise.