  An algebraic approximation, of order $K$, of a polyhedron correlation
function (CF) can be obtained from $\gamma\pp(r)$, its chord-length
distribution (CLD), considering first, within the subinterval $[D_{i-1},\,
D_i]$ of the full range of distances, a polynomial in the two variables
$(r-D_{i-1})^{1/2}$ and $(D_{i}-r)^{1/2}$ such that its expansions around
$r=D_{i-1}$ and $r=D_i$ simultaneously coincide with left and the right
expansions of $\gamma\pp(r)$ around $D_{i-1}$ and $D_i$ up to the terms
$O\big(r-D_{i-1}\big)^{K/2}$ and $O\big(D_i-r\big)^{K/2}$, respectively. Then,
for each $i$, one integrates twice the polynomial and determines the
integration constants matching the resulting integrals at the common end
points. The 3D Fourier transform of the resulting algebraic CF approximation
correctly reproduces, at large $q$s, the asymptotic behaviour of the exact form
factor up to the term $O(q^{-(K/2+4)})$. For illustration, the procedure is
applied to the cube, the tetrahedron and the octahedron.
