A non-involutory selfduality (Q1116093)

A 3-polytope is said to be selfdual provided there exists a bijection f between the set of faces and the set of vertices which is inclusion- reversing. The author gives a simple example of a selfdual polytope which does not admit an involutory selfduality f. This provides the negative answer to a problem by \textit{B. Grünbaum} and \textit{G. C. Shephard} [Am. Math. Mon. 95, No.8, 729-733 (1988; Zbl 0658.52004)].