An equilateral polygon is any polygon whose sides are all the same length. That’s the only requirement: every edge must be equal. The angles, however, can be different from one another. This single distinction separates equilateral polygons from regular polygons and makes the category broader than most people initially expect.
How Equilateral Differs From Regular
Three related terms come up in geometry, and they’re easy to mix up. A polygon is equilateral if all its sides are equal. A polygon is equiangular if all its angles are equal. A polygon is regular if it’s both equilateral and equiangular at the same time. A square, for instance, is regular because its four sides are equal and all four angles are 90°. A rhombus has four equal sides but its angles aren’t all the same, so it’s equilateral but not regular.
This means every regular polygon is automatically equilateral, but not every equilateral polygon is regular. The “equilateral” label is the looser category. It only cares about side lengths and places no constraints on angles.
The Triangle Exception
Triangles are a special case. If you make a triangle with three equal sides, you always get three equal angles of 60° each. There’s no way around it. The proof relies on a basic property of isosceles triangles: when two sides of a triangle are equal, the angles opposite those sides must also be equal. In a triangle with three equal sides, you can apply that rule from every direction, forcing all three angles to match. So for triangles, equilateral automatically means equiangular, which means equilateral triangles are always regular.
This rule breaks down for every polygon with four or more sides. A four-sided shape can have all equal sides while its angles vary widely, and the same is true for pentagons, hexagons, and beyond.
The Rhombus: A Classic Example
The rhombus is the go-to example of an equilateral polygon that isn’t regular. Sometimes called an equilateral quadrilateral, a rhombus has four sides of identical length. But only its opposite angles are equal, not all four. A square is technically a special type of rhombus where all angles happen to be 90°, but tilt those angles even slightly and you lose the equiangular property while keeping all sides equal.
This is why a rhombus can never be classified as a regular polygon. It satisfies the side-length requirement but fails the angle requirement. You can see this clearly by imagining a diamond shape on a playing card: all four edges are the same length, yet the top and bottom angles are sharp while the left and right angles are wide.
Convex and Concave Versions
Equilateral polygons can be either convex or concave. A convex polygon has all its interior angles pointing outward, like a stop sign. A concave polygon has at least one angle that “caves in” toward the center, creating a dent or a point that folds inward. All star shapes, for example, are concave polygons.
You can build an equilateral star by making every edge the same length while alternating between angles that point outward and angles that point sharply inward. The result is a shape where every side is identical but the angles vary dramatically. This is another illustration of why equal sides don’t force equal angles once you move beyond triangles.
Interior Angles Still Follow the Same Rules
The total of all interior angles in any polygon, equilateral or not, follows a simple formula: multiply the number of sides minus two by 180°. A four-sided polygon always has interior angles totaling 360°. A five-sided polygon totals 540°. A six-sided one totals 720°. The formula works by dividing the polygon into triangles. A shape with n sides can always be split into n minus 2 non-overlapping triangles, and since each triangle contains 180° worth of angles, you multiply accordingly.
In a regular polygon, that total is split evenly among all the angles. In an equilateral polygon that isn’t regular, the total stays the same but the individual angles can differ. A rhombus still has angles summing to 360°, but instead of four 90° corners, it might have two angles of 60° and two of 120°.
Calculating the Perimeter
One practical advantage of equilateral polygons is that perimeter calculations become trivial. The perimeter of any polygon is the sum of all its side lengths. When every side is the same length, that simplifies to the number of sides multiplied by the side length. An equilateral hexagon with sides of 5 cm has a perimeter of 30 cm. An equilateral pentagon with sides of 8 inches has a perimeter of 40 inches. No need to measure each side individually.
Inscribed in a Circle
There’s an elegant geometric property worth knowing: any equilateral polygon inscribed in a circle is automatically regular. If you place all the vertices of an equilateral polygon on the circumference of a single circle, the equal side lengths force the angles to be equal as well. This is why constructing regular polygons with a compass and straightedge works so reliably. By anchoring vertices to a circle, the compass guarantees equal spacing, and the equal spacing guarantees both equal sides and equal angles simultaneously.
Outside a circle, though, that constraint disappears. An equilateral polygon whose vertices don’t all sit on a single circle is free to have unequal angles, which is exactly what happens with a rhombus or an equilateral star.