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The purpose of this paper is to study the slices of the Okounkov bodies ofMori dream spaces. First, we analyze all the slices of the Okounkov bodies ofbig divisors on Mori dream spaces associated to some admissible flags. As abyproduct, we obtain their descriptions on Mori dream threefolds. Finally, weconsider its application to the rational polyhedrality of them.

Slices of Okounkov bodies of big divisors on Mori dream spaces