Whilst I can't be bothered, I suspect were it to be redrawn as a 2D diagram, without one arm crossing another, it may reduce to a series of resistances in series and in parallel which can then be calculated a bit at a time.
Neighbour stated had the cube been made up of 1 ohm resistors the answer would be 0.83333 ohms. He mentioned also the way to solve it is by converting the 3D cube into a 2D model representation!!