Equiangular polygon
If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon.
For clarity, a planar equiangular polygon can be called direct or indirect.
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.
Vertices represent the intersection point between pairs of neighboring line.
Each moved line adjusts its edge-length and the lengths of its two neighboring edges.
Odd-sided direct equiangular polygons can only be partially inverted, leaving a mixture of supplementary angles.
For a direct equiangular p/q star polygon, density q, each internal angle is 180(1-2q/p)°, with 1<2q For w=gcd(p,q)>1, this represents a w-wound (p/w)/(q/w) star polygon, which is degenerate for the regular case. Every direct equiangular p-gon can be given a notation or , like regular polygons {p} and regular star polygons {p/q}, containing p vertices, and stars having density q. Convex equiangular p-gons have internal angles 180(1-2/p)°, while direct star equiangular polygons, , have internal angles 180(1-2q/p)°. A concave indirect equiangular p-gon can be given the notation For example, <6-2> is a hexagon with 90° internal angles of the difference, <4>, 1 counter-turned vertex. gives rise to an equiangular n-gon if and only if either of two equivalent conditions holds for the polynomial [5] Direct equiangular polygons can be regular, isogonal, or lower symmetries. Examples for are grouped into sections by p and subgrouped by density q. Equiangular triangles must be convex and have 60° internal angles. An equiangular quadrilateral with integer side lengths may be tiled by unit squares. An equiangular hexagon with integer side lengths may be tiled by unit equilateral triangles. Convex solutions with integer edge lengths may be tiled by pattern blocks, squares, equilateral triangles, and 30° rhombi.
