Quasitoric manifolds and Small covers over properly colored polytopes: Immersions and Embeddings

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We construct small covers and quasitoric manifolds over n-dimensional simple polytopes which allow proper colorings of facets with n colors. We calculate 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.