  The phase diagrams of LaMnO$_3$ perovskites have been intensely studied due
to the colossal magnetoresistance (CMR) exhibited by compositions around the
$\frac{3}{8}^{th}$ doping level. However, phase segregation between
ferromagnetic (FM) metallic and antiferromagnetic (AFM) insulating states,
which itself is believed to be responsible for the colossal change in
resistance under applied magnetic field, has prevented an atomistic-level
understanding of the orbital ordered (OO) state at this doping level. Here,
through the detailed crystallographic analysis of the phase diagram of a
prototype system (AMn$_3^{A'}$Mn$_4^B$O$_{12}$), we show that the superposition
of two distinct lattice modes gives rise to a striping of OO Jahn-Teller active
Mn$^{3+}$ and charge disordered (CD) Mn$^{3.5+}$ layers in a 1:3 ratio. This
superposition only gives a cancellation of the Jahn-Teller-like displacements
at the critical doping level. This striping of CD Mn$^{3.5+}$ with Mn$^{3+}$
provides a natural mechanism though which long range OO can melt, giving way to
a conducting state.
