Unfortunately, there is an error in one of his examples, which leaves an infinite class of immersions with no known examples. In 1993, Cervone [to appear] located and corrected this error in Pinkall's work, and succeeded in producing polyhedral models of several of the classes of immersions for which no tight example was previously known, leaving the situation for only two classes yet to be resolved.
The bibliography also includes references to papers with related results, in particular, to higher-dimensional analogues.
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