Equiangular polygon Equiangular polygon 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. The only equiangular triangle is the equilateral triangle. Rectangles, including the square, are the only equiangular quadrilaterals (four-sided figures). For a convex equiangular "n"-gon each internal angle is 180(1-2/n)°; this is the "equiangular polygon theorem". Viviani's theorem holds for equiangular polygons: A rectangle (equiangular quadrilateral) with integer side lengths may be tiled
Petrie polygon of Petrie polygons was later extended to semiregular polytopes. The Petrie polygon of the regular polyhedron {"p", "q"} has "h" sides, where The regular duals, {"p","q"} and {"q","p"}, are contained within the same projected Petrie polygon. The regular Kepler–Poinsot polyhedra have hexagonal, {6}, and decagrammic, {10/3}, Petrie polygons. Infinite regular skew polygons (apeirogon) can also be defined as being the Petrie polygons of the regular tilings, having angles of 90, 120, and 60 degrees of their square, hexagon and triangular faces respectively. Infinite regular skew polygons also exist as Petrie polygons of the regular hyperbolic tilings, like the order-7 triangular