Subpolytopes of cyclic polytopes (Q1964646)

The authors prove directly that every subpolytope of a cyclic \(d\)-polytope is cyclic. If \(d\) is even, this statement was proven previously by \textit{I.~Shemer} in [Isr. J. Math. 43, 291-314 (1982; Zbl 0598.05010)]. If \(d\) is odd, this result is new but the authors show that it can also be derived from a result of \textit{R.~Cordovil} and \textit{P.~Duchet} [Eur. J. Comb. 21, No. 1, 49-64 (2000)].