Alphabetical Index of Vertex Figure Usages

While facets of uniform polytopes by definition are uniform as well – in fact, the dynkin diagram of a facet of a Wythoffian polytope is derived by omission of just one node (and its incident links) – this does not hold true with respect to vertex figures. On the contrary, most generally the vertex figure of a uniform polytope is not uniform. By means of the concept of lace simplices the vertex figure of Wytoffian polytopes can be derived none the less systematically (as is outlined there).

Accordingly this listing of vertex figure polytopes runs much shorter than that for facets, especially because the following table was generated from the files included in the "incmats" folder. Thus these listings therefore do not aim to be any complete enumeration, they represent only the results from so far in this webspace provided individual polytope files.

Total count of currently listed polytopes, which occur as vertex figures of others: 418

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