Abstract
LetC(ν, d) represent a cyclic polytope withν vertices ind dimensions. A criterion is given for deciding whether a given subset of the vertices ofC(ν, d) is the set of vertices of some face ofC(ν, d). This enables us to determine, in a simple manner, the number ofj-faces ofC(ν, d) for each value ofj (1≦j≦d−1).
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Shephard, G.C. A theorem on cyclic polytopes. Israel J. Math. 6, 368–372 (1968). https://doi.org/10.1007/BF02771216
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DOI: https://doi.org/10.1007/BF02771216