Many years ago i saw an abstract in the Oberwolfach Vortragsbuch entitled "Squares in Lake Michigan", which for a long time I thought proved theorems such as "any Jordan curve - or distorted circle in the plane - contains 4 points which are at the vertices of a square". But I never saw anything more about this, and began to doubt my memory. Just now I found the following on MathSciNet, so maybe it was not a dream: MR0474041 (57 #13698) Fourneau, René; Leytem, Charles Sur l'existence de $n$-losanges réguliers inscrits dans un corps compact convexe. (French) Comment. Math. Univ. Carolinae 19 (1978), no. 1, 151--164. This paper provides a solution for the generalized problem of "squares in Lake Michigan" for some classes of convex sets. The authors show that, in $R^d$, one can inscribe a regular crosspolytope (the generalization of the square and of the regular octahedron) in every compact convex body with an axis of revolution, and in every centrally symmetric compact convex body. In both cases, the uniqueness of such an inscribed regular cross polytope is investigated. NJAS