3D polyhedron with no axis of symmetry In learning to work with inertia tensors I came to wonder if there were any polyhedra with no axis of symmetry; and if so, are there any regular polyhedra ? My workings so far : the only shape I can think of in 3D that has no axis of symmetry is of course an ellipsoid; so I was wondering if this is due to the fact that it has no angles... Thanks and sorry if this is too much of an open question; I'll delete it if needed.

The following polyhedra all have some symmetry – either a rotation axis or a mirror plane (which has an associated normal axis):

*

*Platonic solids and Kepler–Poinsot solids

*Prisms and antiprisms, including star forms

*Archimedean solids and uniform star polyhedra

*Johnson solids

So no regular polyhedron, by any reasonable definition, is wholly asymmetric. However, it is very easy to make such a polyhedron. Just take six distinct edges that differ by any sufficiently small amount – $7,8,9,10,11,12$ will do – and build a tetrahedron with them.
