Relation between crystal structure and optical properties in the correlated blue pigment <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>YIn</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>Mn</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>

A material's properties and functionalities are determined by its chemical constituents the atomic arrangement in which they crystallize. For recently discovered pigment ${\mathrm{YIn}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}{\mathrm{O}}_{3}$, for instance, it had been surmised that bright blue color owes to an unusual, trigonal bipyramidal, oxygen coordination of manganese impurities. Here, we demonstrate that, indeed, a direct correspondence between details local Mn environment pigment's holds: Combining realistic many-body calculations (dynamical mean-field theory treat quasi-atomic Mn-multiplets at low doping $x=8%$) with effective medium description (Kubelka-Munk model describe scattering milled sample), find only Mn-coordination polyhedra consisting two distorted pyramids results diffuse reflectance commensurate experimental color. We motivate distortion bipyramid helps circumventing selection rules, allowing dipolar $d\text{\ensuremath{-}}d$ transitions creating desired two-peak absorption profile.