  We investigate point arrangements $v_i\in\mathbb R^d,i\in \{1,...,n \}$ with
certain prescribed symmetries. The arrangement space of $v$ is the column span
of the matrix in which the $v_i$ are the rows. We characterize properties of
$v$ in terms of the arrangement space, e.g. we characterize whether an
arrangement possesses certain symmetries or whether it can be continuously
deformed into another arrangement while preserving symmetry in the process. We
show that whether a symmetric arrangement can be continuously deformed into its
mirror image depends non-trivially on several factors, e.g. the decomposition
of its representation into irreducible constituents, and whether we are in even
or odd dimensions.
