Show that for any such tesselation, we must have $m \geq 3$ and, using part (a), that $n \leq 6$. In this problem you will discover some very strong restrictions on possible tesselations of the plane, stemming from the fact that that each interior angle of an $n$ sided regular polygon measures $\frac\right) = 360.
Of a regular tessellation which can be continued indefinitely in all directions: The checkerboard pattern below is an example If any two polygons in the tessellation either do not meet, share a vertex only, For non-regular shapes it is necessary that the angles of the shapes can be grouped so that they sum to 360. Only three regular polygons can tessellate the Euclidean plane: triangles, squares, or. the tessellation is a regular tessellation. If all polygons in the tessellation are congruent regular polygons and However a regular Octagon and a square can be used together to make a tessellation. A semiregular or uniform tiling has one type of vertex, but two or more types of faces. Students will also also create their tessellating design by transforming the regular polygons using Escher-like techniques. A regular tiling has one type of regular face. They also create their own tessellating design. Then make a design in the black permanent marker. For example, part of a tessellation with rectangles is Tessellations Overview and Objective In this exploration, students will use the polygons on Polypad to create regular and semi-regular tessellations. Go over the lines with a black permanent marker. A tessellation of the plane is an arrangement of polygons which cover the plane without gaps or overlapping. Non-regular tessellations are those in which there is no restriction on the order of the polygons around vertices.
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