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
Euclidean tilings by convex regular polygons vertex and one has an odd number of sides, the other two polygons must be the same. If they are not, they would have to alternate around the first polygon, which is impossible if its number of sides is odd. By that restriction these six cannot appear in any tiling of regular polygons: These four can be used in "k"-uniform tiling: Some of the "k"-uniform tilings can be derived by symmetrically dissecting the tiling polygons with interior edges, for example: Some k-uniform tilings can be derived by dissecting regular polygons with new vertices along the original edges, for example: There