Neighborly cubical polytopes and spheres
We prove that the neighborly cubical polytopes studied by Günter M. Ziegler and the first named author  arise as a special case of the neighborly cubical spheres constructed by Babson, Billera and Chan . By relating the two constructions we obtain an explicit description of a non-polytopal neighborly cubical sphere and, further, a new proof of the fact that the cubical equivelar surfaces of McMullen, Schulz and Wills  can be embedded into ℝ3.
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