[2] Thus, for instance, the regular octahedron is an example of a centrally symmetric convex shape that is not a zonoid.
[1] The solid of revolution of the positive part of a sine curve is a zonoid, obtained as a limit of zonohedra whose generating segments are symmetric to each other with respect to rotations around a common axis.
[4] The bicones provide examples of centrally symmetric solids of revolution that are not zonoids.
[1] Zonoids are closed under affine transformations,[2] under parallel projection,[5] and under finite Minkowski sums.
Ethan Bolker credits the formulation of this problem to a 1916 publication of Wilhelm Blaschke.