  The Swampland Distance Conjecture proposes that approaching infinite
distances in field space an infinite tower of states becomes exponentially
light. We study this conjecture for the complex structure moduli space of
Calabi-Yau manifolds. In this context, we uncover significant structure within
the proposal by showing that there is a rich spectrum of different infinite
distance loci that can be classified by certain topological data derived from
an associated discrete symmetry. We show how this data also determines the
rules for how the different infinite distance loci can intersect and form an
infinite distance network. We study the properties of the intersections in
detail and, in particular, propose an identification of the infinite tower of
states near such intersections in terms of what we term charge orbits. These
orbits have the property that they are not completely local, but depend on data
within a finite patch around the intersection, thereby forming an initial step
towards understanding global aspects of the distance conjecture in field
spaces. Our results follow from a deep mathematical structure captured by the
so-called orbit theorems, which gives a handle on singularities in the moduli
space through mixed Hodge structures, and is related to a local notion of
mirror symmetry thereby allowing us to apply it also to the large volume
setting. These theorems are general and apply far beyond Calabi-Yau moduli
spaces, leading us to propose that similarly the infinite distance structures
we uncover are also more general.
