Equiangular polygon
| Direct | Indirect | Skew |
|---|---|---|
A rectangle, ⟨4⟩, is a convex direct equiangular polygon, containing four 90° internal angles. |
A concave indirect equiangular polygon, ⟨6-2⟩, like this hexagon, counterclockwise, has five left turns and one right turn, like this tetromino. |
A skew polygon has equal angles off a plane, like this skew octagon alternating red and blue edges on a cube. |
| Direct | Indirect | Counter-turned |
A multi-turning equiangular polygon can be direct, like this octagon, ⟨8/2⟩, has 8 90° turns, totaling 720°. |
A concave indirect equiangular polygon, ⟨5-2⟩, counterclockwise has 4 left turns and one right turn. (-1.2.4.3.2)60° |
An indirect equiangular hexagon, ⟨6-6⟩90° with 3 left turns, 3 right turns, totaling 0°. |
In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths.
For clarity, a planar equiangular polygon can be called direct or indirect. A direct equiangular polygon has all angles turning in the same direction in a plane and can include multiple turns. Convex equiangular polygons are always direct. An indirect equiangular polygon can include angles turning right or left in any combination. A skew equiangular polygon may be isogonal, but can't be considered direct since it is nonplanar.
A spirolateral nθ is a special case of an equiangular polygon with a set of n integer edge lengths repeating sequence until returning to the start, with vertex internal angles θ.