  The Emergent String Conjecture constrains the possible types of light towers
in infinite-distance limits in quantum gravity moduli spaces. In this paper, we
use these constraints to restrict the geometry of the scalar charge-to-mass
vectors $(-\vec{\nabla}\log m)$ of the light towers and the analogous vector
$(-\vec{\nabla}\log\Lambda_{\text{QG}})$ of the species scale. We derive
taxonomic rules that these vectors must satisfy in each duality frame. Under
certain assumptions, this allows us to classify the ways in which different
duality frames can fit together globally in the moduli space in terms of a
finite list of polytopes. Many of these polytopes arise in known string theory
compactifications, while others suggest either undiscovered corners of the
landscape or new swampland constraints.
