The researchers found a 14-sided shape that, like the hat, could tile a surface without creating repeating patterns as long as its reflection was also used. However, ...

It is a reflection of the fundamental structure of the world. ... “It is only by not repeating the pattern that you create real visual diversion,” he says.

The compulsion to repeat is particularly interesting because what is repeated is not pleasurable. On the contrary, it is usually a painful and destructive pattern of feeling and behaving.