A hexagon has six sides and six corners. A pentagon has five, an octagon has eight, and the same counting rule connects every simple polygon to its name. Count the straight segments around the boundary, rather than judging how familiar or symmetrical the shape looks.
This reference covers simple plane polygons: flat, closed outlines made from straight segments that do not cross one another. The photographs are illustrative; use the table below for exact names and counts.
Polygon names and side counts
For these polygons, the number of sides equals the number of vertices, the mathematical word for corners. The table applies to irregular outlines as well as the balanced shapes usually shown in reference books.
| Polygon name | Sides | Vertices |
|---|---|---|
| Triangle | 3 | 3 |
| Quadrilateral | 4 | 4 |
| Pentagon | 5 | 5 |
| Hexagon | 6 | 6 |
| Heptagon | 7 | 7 |
| Octagon | 8 | 8 |
| Nonagon (enneagon) | 9 | 9 |
| Decagon | 10 | 10 |
| Hendecagon (undecagon) | 11 | 11 |
| Dodecagon | 12 | 12 |
| n-gon | n | n |
In n-gon, n stands for the side count. For a simple plane polygon, n is a whole number of at least three. You can say “11-gon” if you do not remember hendecagon. Alternative names such as nonagon and enneagon describe the same count, not different shapes. Wolfram MathWorld’s polygon reference lists these names and alternatives.
What counts as a side or a corner?
A side is one straight segment between neighboring vertices. A vertex is the meeting point where the boundary changes direction. Trace the outline once, moving from corner to corner, and stop when you return to your starting point. Do not count that starting corner twice.
Imagine a flat panel with corners labeled A, B, C, D, E and F in order. Its boundary consists of AB, BC, CD, DE, EF and FA: six segments, making a hexagon. A line drawn from A across the interior to D does not add a side. It divides the drawing visually, but it is not part of the outside boundary.
Likewise, a mark halfway along a straight side does not create another geometric corner. If the boundary continues in exactly the same direction, treat it as the same side. Check the actual outline rather than paint lines, seams, shadows or printed decoration.
Regular and irregular describe more than the count
A regular polygon has equal side lengths and equal interior angles. Both conditions matter. An irregular polygon fails one or both of those conditions, but its side-count name stays the same. A six-sided outline with one short edge is still a hexagon.
A square is a regular quadrilateral. A non-square rectangle has equal angles but unequal adjacent side lengths, so it is not regular. A non-square rhombus has equal sides but unequal angles, so equal sides alone are not enough either. MathWorld’s regular-polygon definition makes the two requirements explicit.
This distinction is useful when reading a product description or architectural drawing. “Hexagonal” tells you the outline has six sides; “regular hexagonal” adds information about its proportions. Do not assume a tidy illustration guarantees equal measurements when dimensions or specifications say otherwise.
Convex and concave describe the outline
A convex polygon has no inward indentation. More precisely, a straight segment joining any two points in the filled polygon stays within it. A concave polygon has an inward corner: at least one interior angle exceeds 180 degrees. These definitions are explained in MathWorld’s convex and concave polygon entries.
A simple six-sided outline can be convex or concave. Pushing one corner inward can change that classification without changing the number of sides, provided the outline remains simple and no sides disappear. Count inward corners too. Looking only at the outward tips can give the wrong answer.
Star drawings need extra care. A filled star silhouette with a noncrossing boundary can be counted as a concave polygon, but a star drawn with crossing strokes uses a different construction. This table is not a guide to self-intersecting star polygons. Decide which outline you mean before counting.
Turning the shape does not rename it
A square remains a square when it rests on a corner. A hexagon remains a hexagon whether a flat edge or a point faces upward. Rotation changes orientation, not side count, side lengths or angles. The casual word “diamond” does not supply enough information to decide whether an outline is a square or another rhombus.
Photographs introduce another complication: perspective can make equal edges look unequal. If you need to establish regularity, use the object’s dimensions or a suitable straight-on drawing instead of measuring an angled photo. For a partially hidden outline, do not guess the missing corners from the visible ones.
Keep flat outlines separate from solid objects
Polygon sides belong to a two-dimensional outline. A solid object has faces, edges and vertices, which answer different counting questions. A hexagonal face on a solid has six boundary sides, but that does not tell you how many faces the entire object has.
A circle or oval has a curved boundary, so neither is a polygon in this reference. Rounded corners also mean a manufactured object is only an approximation of the ideal straight-edged shape. Describe that distinction when precision matters.
If your next question is the distance around the outline, see our circumference and perimeter guide. For a printed reference with clearly labeled drawings, you can also browse geometry reference books on Amazon.
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