“a polygon with 120-degree angles at the corners actually has four sides instead of six,”
http://www.johnspeedie.com/healy/okay.wav
Put a point on a sphere and make 3 lines from it 120 degrees apart. extend 2 of the lines from that point form part of a great circle. now there will be 2 other points you can put on those lines that will have similar great arcs that intersect at the 4th point.