#Non regular octagon tessellation series

Can you create a regular tessellation with a regular pentagon? Of all tessellations of the plane which include regular heptagons, I think this is the one which minimizes between-heptagon gap-size (the parts of the plane outside any heptagon). Regular heptagons, of course, can’t tile a plane by themselves. The corresponding holes are shaped decagon, hexagon, square, and triangle.

We can see from this that the pentagon, hexagon, octagon, and dodecagon tesselate with one skipped vertex. You can even tessellate pentagons, but they won’t be regular ones. You can have other tessellations of regular shapes if you use more than one type of shape. Triangles, squares and hexagons are the only regular shapes which tessellate by themselves. These octagons have four pairs of parallel sides. The underlying pattern of this tiling is just a grid. I guess even though these shapes have eight sides each, they’re really just parallelograms or rectangles in disguise. You can’t tile the Euclidean plane with regular octagons. Only three regular polygons (shapes with all sides and angles equal) can form a tessellation by themselves- triangles, squares, and hexagons.

#Non regular octagon tessellation series

Not only do they not have angles, but you can clearly see that it is impossible to put a series of circles next to each other without a gap. What shapes Cannot tessellate?Ĭircles or ovals, for example, cannot tessellate. From this, we know that a regular octagon will not tessellate by itself because 135? does not go evenly into 360?. Why a regular octagon does not tessellate?Įach angle in a regular pentagon is 1080?÷8=135?. Two octagons have angle measures that sum to 270° (135° + 135°), leaving a gap of 90°. It is not possible to tile the plane using only octagons. Is it possible to use only an octagon to create a tessellation?