Regular heptagons, of course, can't tile a plane by themselves. ... The shape of each of the polygons which fill the “heptagon-only gaps” is a biconcave, equilateral octagon. With these octagons, this is a tessellation, but without them, it wouldn't fit the definition of that term.

Why does a regular Heptagon not tessellate?

Can a Heptagon Tessellate? No, A regular heptagon (7 sides) has angles that measure (n-2)(180)/n, in this case (5)(180)/7 = 900/7 = 128.57. A polygon will tessellate if the angles are a divisor of 360. The only regular polygons that tessellate are Equilateral triangles, each angle 60 degrees, as 60 is a divisor of 360.

Is it possible to create a regular tessellation with a regular Heptagon?

Regular tessellations The simplest kind of tessellation is called a regular tessellation, in which we cover the plane entirely with copies of a single shape that has equal sides. ... It's impossible to tessellate with regular pentagons (5 sides), heptagons (7 sides), octagons (8 sides) or any other number.