  Artificial particle ices are model systems of constrained, interacting
particles. They have been introduced theoretically to study ice-manifolds
emergent from frustration, along with domain wall and grain boundary dynamics,
doping, pinning-depinning, controlled transport of topological defects,
avalanches, and memory effects. Recently such particle-based ices have been
experimentally realized with vortices in nano-patterned superconductors or
gravitationally trapped colloids. Here we demonstrate that, although these ices
are generally considered equivalent to magnetic spin ices, they can access a
novel spectrum of phenomenologies that are inaccessible to the latter. With
experiments, theory and simulations we demonstrate that in mixed coordination
geometries, entropy-driven negative monopoles spontaneously appear at a density
determined by the vertex-mixture ratio. Unlike its spin-based analogue, the
colloidal system displays a "fragile ice" manifold, where local energetics
oppose the ice rule, which is instead enforced through conservation of the
global topological charge. The fragile colloidal ice, stabilized by topology,
can be spontaneously broken by topological charge transfer.
