English: The 24 vertices of the 24-cell are distributed at four different chord lengths from each other: √1, √2, √3, or √4. The √1 edges occur in 16 hexagonal great circles. The √2 chords occur in 18 square great circles. The √3 chords occur in 32 triangular great circles. The √4 chords occur as 12 vertex-to-vertex diameters, the 24 radii around the 25th central vertex.