  For each cardinal $\kappa$, each natural number $n$ and each simplicial
complex $K$ we construct a space $\nu^n_\kappa(K)$ and a map $\pi \colon
\nu^n_\kappa(K) \to K$ such that the following conditions are satisfied.
  1. $\nu^n_\kappa(K)$ is a complete metric $n$-dimensional space of weight
$\kappa$.
  2. $\nu^n_\kappa(K)$ is an absolute neighborhood extensor in dimension $n$.
  3. $\nu^n_\kappa(K)$ is strongly universal in the class of $n$-dimensional
complete metric spaces of weight~$\kappa$.
  4. $\pi$ is an $n$-homotopy equivalence.
  For $\kappa = \omega$ the constructed spaces are $n$-dimensional separable
N\"obeling manifolds. The constructed spaces have very interesting fractal-like
internal structure that allows for easy construction, subdivision, and surgery
of brick partitions.
