2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71287This is an overview of results from our experiment of merging two seemingly unrelated disciplines - higher algebraic K-theory of rings and the theory of lattice polytopes. The usual K-theory is the ``theory of a unit simplex''. A conjecture is proposed on the structure of higher polyhedral K-groups for certain class of polytopes for which the coincidence of Quillen's and Volodin's theories is known.final version, to appear in Georg. Math. JK-Theory and HomologyAlgebraic GeometryPrimany: 19C09, 19D06, 19M05; Secondary: 14M25, 52B20text