@CardColm If I'm not mistaken (and I might well be, this is *X in the orbifold notation: lining up everything that's the same, you'd have a great thickened up Möbius band, if you could actually manage it!
Ok, if you think about, you can see why the upright hand in the back is also a right hand— this is the “mirror paradox”, that you’re not reversed in a pair of mirrors meeting in a right angle.
So why is the ipad backwards?
The lamplighter group as a limit of groups: L1 is drawn on ideal squares in H2.
L2, shown here sits on ideal cubes in H3. Rolling these up by the next relator for L3 gives a graph on ideal hypercubes in H4, etc,
Limiting to the #lamplightergroup#symmetry#mathbun