but why is it so messy?

Menu > View > Hidden Geometry will show hidden/smoothed edges so you can edit or snap to them. With them showing you can now draw lines onto the surfaces to make new areas and then add another colour to these 'stripe' faces... There's also a plugin called 'lines/tools on surface' that lets you do this more easily... Remember to switch off 'Hidden Geometry' when you are done... Make sure your Style includes showing edges !

What I would guess is that those facets aren't coplanar therefore SU also triangulates them. Try to delete one of the diagonal edges and if the face also disappears, this is the problem. Another way would be to use the text tool (make sure your import is ungrouped or you are editing it if grouped) to learn what the co-ordinates of the vertical edges are. Place the text tool on an endpoint of any of these edges then on the other endpoint. By default, the text tool will show the x,y,z co-ordinates the two first of which should be the same for those edges.