  We construct and study stationary, asymptotically flat multicenter solutions
describing regular black holes with non-Abelian hair (colored magnetic-monopole
and dyon fields) in two models of $\mathcal{N}=2,d=4$ Super-Einstein-Yang-Mills
theories: the quadratic model $\overline{\mathbb{CP}}^{3}$ and the cubic model
ST$[2,6]$, which can be embedded in 10-dimensional Heterotic Supergravity.
These solutions are based on the multicenter dyon recently discovered by one of
us, which solves the SU$(2)$ Bogomol'nyi and dyon equations on
$\mathbb{E}^{3}$. In contrast to the well-known Abelian multicenter solutions,
the relative positions of the non-Abelian black hole centers are unconstrained.
  We study necessary conditions on the parameters of the solutions that ensure
the regularity of the metric. In the case of the $\overline{\mathbb{CP}}^{3}$
model we show that it is enough to require the positivity of the "masses" of
the individual black holes, the finiteness of each of their entropies and their
superadditivity. In the case of the $ST[2,6]$ model we have not been able to
show that analogous conditions are sufficient, but we give an explicit example
of a regular solution describing thousands of non-Abelian dyonic black holes in
equilibrium at arbitrary relative positions.
  We also construct non-Abelian solutions that interpolate smoothly between
just two aDS$_{2}\times$S$^{2}$ vacua with different radii (dumbbell
solutions).

High Energy Physics - Theory;General Relativity and Quantum Cosmology