Three mutual perpendiculars were not an option, given the initial axes, so this is not a cube.
A first hexahedron.
This one builds flat.
A squashed zero-volume hexahedron. These count.
Removing extra edges.
The third possible hexahedron, starting with the 60-120 rhombus.
Not zero volume.
Adding to the zero volume base plate.
A zonohedron is born of four hexahedra. An hexagonal prism.
A rhombic dodecahedron in disguise.
\A rhombic dodecahedron in disguise.
