About

I've loved the number seven and heptagons for as long as I can remember. I like the exact symmetry of a regular heptagon and the fact that its interior angles aren't whole numbers of degrees.

Here are seven properties I like.

• Each interior angle is exactly 900 ÷ 7 degrees, a rational number with a repeating decimal expansion.
• A heptagon has fourteen diagonals.
• A regular heptagon has seven lines of reflection symmetry. Its sevenfold rotational symmetry means it matches itself after each 360 ÷ 7 degree turn.
• The regular heptagon is the regular polygon with the fewest sides that cannot be constructed exactly using only a compass and an unmarked straightedge. Origami can construct it by solving the underlying cubic equation.
• The decimal expansion of one seventh repeats 142857. Multiplying 142857 by an integer from two through six rotates those digits.
• Seven is a Mersenne prime, a prime number that is one less than a power of two. It equals 2³ − 1.
• Seven is the only dimension besides three that supports a nonzero bilinear vector cross product with the usual perpendicularity and magnitude properties.

The calculated coordinates of every heptagon on this website are rounded to seven decimal places.