  A construction of algebraic surfaces based on two types of simple
arrangements of lines, containing the prototiles of substitution tilings, has
been proposed recently. The surfaces are derived with the help of polynomials
obtained from products of the lines generating the simple arrangements. One of
the arrangements gives the generalizations of the Chebyshev polynomials known
as folding polynomials. The other produces a family of polynomials having more
critical points with the same critical values, which can also be used to derive
hypersurfaces with many Aj-singularities.
