  We discuss statistics of vortices having zero-energy non-Abelian Majorana
fermions inside them. Considering the system of multiple non-Abelian vortices,
we derive a non-Abelian statistics that differs from the previously derived
non-Abelian statistics. The new non-Abelian statistics presented here is given
by a tensor product of two different groups, namely the non-Abelian statistics
obeyed by the Abelian Majorana fermions and the Coxeter group. The Coxeter
group is a symmetric group related to the symmetry of polytopes in a
high-dimensional space. As the simplest example, we consider the case in which
a vortex contains three Majorana fermions that are mixed with each other under
the SO(3) transformations. We concretely present the representation of the
Coxeter group in our case and its geometrical expressions in the
high-dimensional Hilbert space constructed from non-Abelian Majorana fermions.
