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
Euclidean tilings by convex regular polygons first flag to the second. This is equivalent to the tiling being an edge-to-edge tiling by congruent regular polygons. There must be six equilateral triangles, four squares or three regular hexagons at a vertex, yielding the three regular tessellations. Vertex-transitivity means that for every pair of vertices there is a symmetry operation mapping the first vertex to the second. If the requirement of flag-transitivity is relaxed to one of vertex-transitivity, while the condition that the tiling is edge-to-edge is kept, there are eight additional tilings possible, known as "Archimedean", "uniform" or "semiregular" tilings. Note that there are two mirror image