I am trying to find some literature discussing zonoid in 3-dimensional space. And a seemly simple question that I am considered specifically is what are those non-trivial (not being a zonohedron) zonoid are in 3d?
All ellipsoids seems to be zonoid in 3d, but is it ture that this is the only familarly of non-trivial zonoid in 3d? If so, is there an elegant way of proving that? if not, is there a counter-example? or any way to construct more different zonoid?