The chords (the diagonals of the pentagons) form the legs of 720 central isosceles triangles (144 sets of 5 inscribed in each pentagon), 6 of which cross at each vertex. The third edge (base) of each isosceles triangle is an edge of the pentagon of length , so these are golden triangles. The chords run vertex-to-every-fourth-vertex in the same planes as the 72 decagons, joining vertices which are four edges apart on a geodesic great circle. There are 720 distinct chords, in 360 parallel pairs, apart.