So that's how it works for four sides. But for a pentagon, a five-sided shape, it turns out you need nine dots. For a hexagon, it's 17 dots. But beyond that, we don't know. It's a mystery how many dots is required to create a heptagon or any larger shapes. More importantly, there should be a formula to tell us how many dots are required for any shape. Mathematicians suspect the equation is M=1+2 N-2 , where M is the number of dots and N is the number of sides in the shape. But as yet, they've only been able to prove that the answer is at least as big as the answer you get that way.