  Cooperative Jahn-Teller ordering is well-known to drive the cubic
$Fd\overline{3}m$ to tetragonal $I$4$_1$/$amd$ structural distortion in
Mn$_3$O$_4$ at 1170 $^{\circ}$C. Further structural distortion occurs in
Mn$_3$O$_4$ upon magnetic ordering at 42 K. Employing high-resolution
variable-temperature synchrotron x-ray diffraction we show that tetragonal
$I$4$_1$/$amd$ and orthorhombic $Fddd$ phases coexist, with nearly equal
fractions, below the N\'eel temperature of Mn$_3$O$_4$. Significant variation
of the orthorhombic $a$ and $b$ lattice constants from the tetragonal $a$
lattice constant is observed. Structural phase coexistence in Mn$_3$O$_4$ is
attributed to large strains due to the lattice mismatch between the tetragonal
$I$4$_1$/$amd$ and the orthorhombic $Fddd$ phases. Strain tensors determined
from Rietveld refinement show a highly strained matrix of the $I4_1/amd$ phase
that accommodates the nucleated orthorhombic $Fddd$ phase in the phase
coexistence regime. A comparison of the deformation observed in Mn$_3$O$_4$ to
structural deformations of other magnetic spinels shows that phase coexistence
may be a common theme when structural distortions occur below 50 K.
