I bet the vertices are correct, but shouldn't the lines in between them look like curves? They are projected solutions for the points that are equidistant by great circle distance to two airports, so I think they should themselves be great circle arcs.
They are great-circle arcs, but the presentation is a projected sphere, so the lines in the center will look straight because you're looking down on the curved part. Zoom out and look at the lines near the edges.
