The chords form 450 central squares (25 disjoint sets of 18), 15 of which cross at each vertex (3 from each of five 24-cells). Each set of 18 squares consists of the 72 edges and 24 vertices of one of the 25 overlapping inscribed 24-cells. The chords join vertices which are three edges apart (and two chords apart). Each chord is the long diameter of an octahedral cell in just one 24-cell. There are 1800 chords, in 900 parallel pairs, apart.