  A material's properties and functionalities are determined by its chemical
constituents and the atomic arrangement in which they crystallize. For the
recently discovered pigment YIn$_{1-x}$Mn$_x$O$_3$, for instance, it had been
surmised that its bright blue color owes to an unusual, trigonal bipyramidal,
oxygen coordination of the manganese impurities. Here, we demonstrate that,
indeed, a direct correspondence between details of the local Mn environment and
the pigment's blue color holds: Combining realistic many-body calculations
(dynamical mean-field theory to treat the quasi-atomic Mn-multiplets at low
doping x=0.08) with an effective medium description (Kubelka-Munk model to
describe scattering in a milled pigment sample), we find that only a
Mn-coordination polyhedra consisting of two distorted oxygen pyramids results
in a diffuse reflectance commensurate with the experimental blue color. We
motivate that the distortion of the bipyramid helps circumventing atomic
selection rules, allowing for dipolar $d$-$d$ transitions and creating the
desired two-peak absorption profile.
