  A finite-dimensional CAT(0) cube complex $X$ is equipped with several
well-studied boundaries. These include the Tits boundary (which depends on the
CAT(0) metric), the Roller boundary (which depends only on the combinatorial
structure), and the simplicial boundary (which also depends only on the
combinatorial structure). We use a partial order on a certain quotient of the
Roller boundary to obtain the simplicial Roller boundary. Then, we show that
the Tits, simplicial, and simplicial Roller boundaries are all homotopy
equivalent, $Aut(X)$--equivariantly up to homotopy. As an application, we
deduce that the perturbations of the CAT(0) metric introduced by Qing do not
affect the equivariant homotopy type of the Tits boundary. Along the way, we
develop a self-contained exposition providing a dictionary among different
perspectives on cube complexes.
