Quasitoric manifolds and small covers over properly coloured polytopes: immersions and embeddings

We construct small covers and quasitoric manifolds over $n$-dimensional simple polytopes which allow proper colourings of facets with $n$ colours. We calculate the Stiefel-Whitney classes of these manifolds as obstructions to immersions and embeddings into Euclidean spaces. The largest dimension required for embedding is achieved in the case $n$ is a power of two.
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