  We discuss vacua, walls and three-pronged junctions of the mass-deformed
nonlinear sigma models on the Grassmann manifold
$G_{N_F,N_C}=\frac{SU(N_F)}{SU(N_C)\times SU(N_F-N_C)\times U(1)}$, which are
non-Abelian gauge theories for $N_C\geq 2$. Polyhedra are proposed in
\cite{Eto:2005cp} to describe Bogomol'nyi-Prasad-Sommerfield objects of the
mass-deformed nonlinear sigma models on the complex projective space, which are
Abelian gauge theories. We show that we can produce similar polyhedra for the
mass-deformed nonlinear sigma models on the Grassmann manifold by applying the
moduli matrix formalism \cite{Isozumi:2004jc} and the pictorial representation
\cite{Lee:2017kaj}. Non-Abelian junctions can be analysed by making use of the
polyhedra instead of the Pl\"{u}cker embedding. We present diagrams for vacua,
walls and three-pronged junctions, and compute three-pronged junction positions
of the mass-deformed nonlinear sigma models on the Grassmann manifold. We show
that the results are consistent with the known results of \cite{Eto:2005fm},
which are worked out by using the Pl\"{u}cker embedding.
