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Given a complex algebraic hypersurface~$H$, we introduce a polyhedral complexwhich is a subset of the Newton polytope of the defining polynomial for~$H$ andenjoys the key topological and combinatorial properties of the amoeba of~$H.$We provide an explicit formula for this polyhedral complex in the case when thespine of the amoeba is dual to a triangulation of the Newton polytope of thedefining polynomial. In particular, this yields a description of the polyhedralcomplex when the hypersurface is optimal.

Amoeba-shaped polyhedral complex of an algebraic hypersurface