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The Structure Theorem of Tropical geometry states that

"Let $X$ be an irreducible $d$-dimensional subvariety of $\mathbb T^n$ . Then $\operatorname{trop}(X)$ is the support of a balanced weighted $Γ_{\rm val}$ -rational polyhedral complex pure of dimension $d$. If $\operatorname{char}(K) = 0$ then this complex is connected in codimension-one."

What does the term "balanced weighted polyhedral complex" mean in the above theorem?

And suppose I have a subvariety of the algebraic torus. How do I determine the weights of its tropicalization?

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