TITLE: Universal cover of a figure eight?
QUESTION [5 upvotes]: An example in my lecture notes says, 'draw a simply connected covering space over the figure eight'. 
Howerver, after googling, wikipedia tells me that ''The universal cover of the figure eight can be visualized by the Cayley graph'' but I can't see how this graph is simply connected?
NOR, how I am supposed to draw it?
Is there a simple 'draw-able' universal cover of the figure-eight?

REPLY [10 votes]: Here is a picture of the universal cover of a figure eight I made for a topology course in 1991 (!), using Macintosh-Pascal. Note the self-similarity of the "ends".