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
Hyperbolic geometry to tessellate the hyperbolic plane with regular polygons as faces. There are an infinite number of uniform tilings based on the Schwarz triangles (p q r) where 1/p + 1/q + 1/r < 1, where p,q,r are each orders of reflection symmetry at three points of the fundamental domain triangle, the symmetry group is a hyperbolic triangle group. There are also infinitely many uniform tilings that cannot be generated from Schwarz triangles, some for example requiring quadrilaterals as fundamental domains. Though hyperbolic geometry applies for any surface with a constant negative Gaussian curvature, it is usual to assume a scale