Gantry extrusion shape

[Voicecoil]

Well it looks like I'm going to have to bite the bullet and make myself a router, if only because I can't find any ready made ones that will fit through the tiny door to my workshop - it'll be fun as well of course, and I'll understand and be able to maintain it . I've started by going through all the sums on rigidity & weight using @routercnc's calculator and some civil engineering tools, it's amazing how much more interesting moments and such stuff are when you're applying them to a real project rather than in a boring physics lesson. Now one interesting thing that's come out of this is that a square gantry extrusion (say 120 x 120) has a greater torsional rigidity than a rectangular of roughly equal weight/cost (160 x 80). Torsional rigidity seems to be the dominant source of tool error if you have a decent Z travel, so I'm wondering whether there's other reasons why normally such beams tend to be rectangular??? One thing that springs to mind is the reduced distance between the X axis* rails, anyone know how important this would be please?

*I'm taking X axis to be the travel along the gantry looking at the front of the machine.