Congruence (geometry) size. (Most definitions consider congruence to be a form of similarity, although a minority require that the objects have different sizes in order to qualify as similar.) For two polygons to be congruent, they must have an equal number of sides (and hence an equal number—the same number—of vertices). Two polygons with "n" sides are congruent if and only if they each have numerically identical sequences (even if clockwise for one polygon and counterclockwise for the other) side-angle-side-angle-... for "n" sides and "n" angles. Congruence of polygons can be established graphically as follows: If at any time the step cannot
Regular polyhedron five have C×S symmetry but can only be realised with half the symmetry, that is C×A or icosahedral symmetry. They are all topologically equivalent to toroids. Their construction, by arranging "n" faces around each vertex, can be repeated indefinitely as tilings of the hyperbolic plane. In the diagrams below, the hyperbolic tiling images have colors corresponding to those of the polyhedra images. The Petrie dual of a regular polyhedron is a regular map whose vertices and edges correspond to the vertices and edges of the original polyhedron, and whose faces are the set of skew Petrie polygons. The usual nine