  In this paper we study non-negatively curved and rationally elliptic GKM$_4$
manifolds and orbifolds. We show that their rational cohomology rings are
isomorphic to the rational cohomology of certain model orbifolds. These models
are quotients of isometric actions of finite groups on non-negatively curved
torus orbifolds.
  Moreover, we give a simplified proof of a characterisation of products of
simplices among orbit spaces of locally standard torus manifolds. This
characterisation was originally proved in [Wiemeler, Torus manifolds and
non-negative curvature, arXiv:1401.0403] and was used there to obtain a
classification of non-negatively curved torus manifolds.
