The chord-length probability density of the regular octahedron

The chord-length probability density of the regular octahedron is separated into three contributions, relating to the pairs of facets opposite to each other or sharing an edge or a vertex. Each of these contributions is explicitly evaluated throughout the full range of distances and the final expressions only involve inverse trigonometric functions of elementary algebraic functions. Since the chord-length probability density is proportional to the second derivative of the correlation function, knowledge of the chord-length probability density makes the numerical evaluation of the associated small-angle scattering intensity very fast and accurate.