That is, because we are only discussing objects when situated in a minimal embedding space (even an otherwise empty one) wherein all coordinates are given Cartesian values, the axis of rotational symmetry or plane of reflectional symmetry are those denoted in the world, not of the object.
a tetrahedron-which in isolation has seven axes of rotational symmetry, no two of which are orthogonal-when placed in the MES such that it cognitively satisfies all "real-world" constraints, must be situated with one base downward (a tetrahedron placed any other way will fall over).