Δ-graphs of polyhedra in the Bruns-Gubeladze *K*-theory / *M. V. Prikhod'ko.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2013. № 6. P. 19-24
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

W. Bruns and J. Gubeladze introduced a new variant of algebraic *K*-theory, where *K*-groups are additionally parametrized by polytopes of some type.
In this paper we propose a notion of stable *E*-equivalence which can be used to calculate *K*-groups for high-dimensional polytopes.
Polytopes which are stable *E*-equivalent have similar inner structures and isomorphic *K*-groups.
In addition, for each polytope we define a Δ-graph which is an oriented graph being invariant under a stable *E*-equivalence.

*Key words*:
algebraic *K*-theory, balanced polytopes, *E*-equivalence.