Regular polygon is denoted by its Schläfli symbol {"n"}. For "n" < 3, we have two degenerate cases: In certain contexts all the polygons considered will be regular. In such circumstances it is customary to drop the prefix regular. For instance, all the faces of uniform polyhedra must be regular and the faces will be described simply as triangle, square, pentagon, etc. For a regular convex "n"-gon, each interior angle has a measure of: and each exterior angle (i.e., supplementary to the interior angle) has a measure of formula_5 degrees, with the sum of the exterior angles equal to 360 degrees or
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