  Let k be a regular F_p-algebra, let A = k[x,y]/(x^b - y^a) be the coordinate
ring of a planar cuspical curve, and let I = (x,y) be the ideal that defines
the cusp point. We give a formula for the relative K-groups K_q(A,I) in terms
of the groups of de Rham-Witt forms of the ring k. At present, the validity of
the formula depends on a conjecture that concerns the combinatorial structure
of a new family of polytopes that we call stunted regular cyclic polytopes. The
polytopes in question appear as the intersections of regular cyclic polytopes
with (certain) linear subspaces. We verify low-dimensional cases of the
conjecture. This leads to unconditional new results on K_2 and K_3 which extend
earlier results by Krusemeyer for K_0 and K_1.
