A tessellation is a tiling that repeats. ... There are only three regular shapes that tessellate – the square, the equilateral triangle, and the regular hexagon. All other regular shapes, like the regular pentagon and regular octagon, do not tessellate on their own.

Why will a regular octagon not tessellate?

Why or why not? It is not possible to tile the plane using only octagons. Two octagons have angle measures that sum to 270° (135° + 135°), leaving a gap of 90°. Three octagons surrounding a point on the plane would have angle measures that sum to 405°, which would cause an overlap of 45°.

Which regular shapes will tessellate?

Only three regular polygons (shapes with all sides and angles equal) can form a tessellation by themselves—triangles, squares, and hexagons.