Section 12-5 1 Math 366 Lecture Notes Section 12.5 - Tessellations of the Plane A tessellation of a plane (or space) is the filling of the plane (or space) with repetitions of figures in such a way that no figures overlap and there are no gaps. John Locke M.C. Escher A regular tessellation is a tessellation made up of one type of regular polygon. Which regular polygons tessellate the plane? If a regular polygon tessellates the plane, the sum of the congruent angles of the polygons around every vertex must be 360°. Semiregular Tessellations When more than one type of regular polygon is used and the arrangement of the polygons at each vertex is the same the tessellation is semiregular. Section 12-5 2 Other types of polygons can tessellate the plane. ...