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In this work, we explore the relation between the tropicalization of a realsemi-algebraic set $S = \{ f_1 < 0, \dots , f_k < 0\}$ defined in the positiveorthant and the combinatorial properties of the defining polynomials $f_1,\dots, f_k$. We describe a cone that depends only on the face structure of theNewton polytopes of $f_1, \dots ,f_k$ and the signs attained by thesepolynomials. This cone provides an inner approximation of the realtropicalization, and it coincides with the real tropicalization if $S = \{ f <0\}$ and the polynomial $f$ has generic coefficients. Furthermore, we show thatfor a maximally sparse polynomial $f$ the real tropicalization of $S = \{ f <0\}$ is determined by the outer normal cones of the Newton polytope of $f$ andthe signs of its coefficients. Our arguments are valid also for signomials,that is, polynomials with real exponents defined in the positive orthant.

Real tropicalization and negative faces of the Newton polytope