Klein bottle hat in 4-D

I didn't realize when I snapped this photo of my uncle wearing his new Klein bottle hat (aka "knitted representation of a Klein bottle") that a bit of the 4th dimension snuck in:


He was very pleased, but I had the feeling that if I had not made him a Klein bottle hat, he would have been disappointed. He had only mentioned to me once that some of his colleagues had them! Apparently they are de rigeur in academic math circles. Clearly, I have set the bar way too high.