The Relativity of a Staircase

I was blown over by Escher's work when I saw an exhibition in the Fangoch Museum. He didn't know about Swedish artist Oscar Rites-Fard who had done things very similar earlier. So my father and I wrote an article on how he developed the staircase, which was his actually. And then a little while later, he wrote to me and said he'd seen how to do it. But he wants to know what the underlying principle was. It took me a little while before I got back to him. The only tiling that he ever did is what's called non-isahhedral - you can have different instances of the same shape but they're not all periodic