Why Do Some Spirolaterals Never Close?

A simple spirolateral has turns all the same direction. It is denoted by n_θ, where n is the number of sequential integer edge lengths and θ is the internal angle, as any rational divisor of 360°. ... If d = n, the pattern never closes.

Will Spirolaterals always repeat after 12 turns?

So every spirolateral based on three distances will loop back to its starting point after 12 moves.

How do spirolaterals work?

Spirolaterals are geometrical figures formed by the repetition of a simple rule. The base pattern is formed by drawing line segments of increasing length (in integer units) up to a particular size, turning a fixed angle after each segment (clockwise or anti-clockwise).