The chords form 400 equilateral central triangles (25 sets of 32, with each triangle in two sets), 10 of which cross at each vertex (4 from each of five 24-cells, with each triangle in two of the 24-cells). Each set of 32 triangles consists of the 96 chords and 24 vertices of one of the 25 overlapping inscribed 24-cells. The chords run vertex-to-every-second-vertex in the same planes as the 200 hexagons: two triangles are inscribed in each hexagon. The chords join vertices which are four edges apart (and two chords apart on a geodesic great circle). Each chord is the long diameter of two cubic cells in the same 24-cell. There are 1200 chords, in 600 parallel pairs, apart.