Skew polygon Skew polygon In geometry, a skew polygon is a polygon whose vertices are not all coplanar. Skew polygons must have at least 4 vertices. The "interior" surface (or area) of such a polygon is not uniquely defined. Skew infinite polygons (apeirogons) have vertices which are not all collinear. A zig-zag skew polygon or antiprismatic polygon has vertices which alternate on two parallel planes, and thus must be even-sided. Regular skew polygon in 3 dimensions (and regular skew apeirogons in 2 dimensions) are always zig-zag. A regular skew polygon is isogonal with equal edge lengths. In 3 dimensions a regular skew
Skew apeirogon they can be called quasiregular. Example quasiregular skew apeirogons can be seen in the Euclidean tilings as truncated Petrie polygons in truncated regular tilings: In hyperbolic geometry, regular skew apeirogons are similarly found like in the Euclidean plane. Hyperbolic regular skew apeirogons also exist as Petrie polygon zig-zagging edge paths on all of the regular tilings of the hyperbolic plane. And again like Euclidean space, hyperbolic quasiregular skew apeirogons can be constructed as truncated petrie polygons within the edges of a truncated regular tiling. A helical skew apeirogon can exist in three dimensions, where the vertices can be seen as