Abstract

In [5] Bruns and Gubeladze have constructed Milnor K 2-groups for so-called balanced lattice polytopes and classified the balanced polytopes of dimension 2 up to equivalence of the stable elementary groups 𝔼(R, P). In [6] they have shown that the polytopes in a certain subclass, called Col-divisible, behave well for the construction of higher K-groups. In this article, we give a list of all possibly occurring E-equivalence classes of three-dimensional balanced polytopes. Finally, we compute 𝔼(R, P) provided P is a Col-divisible balanced polytope of dimension three.

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