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

On the K-theory of planar cuspical curves and a new family of polytopes