Maybe someone who knows more about structures can comment, but I guess the big issue is how rigid the joints are. A triangulated structure is good because the joints don't need to be fixed--they can be hinged pin-joints and the frame is still rigid + easier to calculate structurally. But if the joints are very rigid, you can go with slightly less efficient option of rectangular framing if that's more convenient.
In architecture it's sometimes called a Vierendeel truss, https://en.wikipedia.org/wiki/Vierendeel_bridge
and it's very handy for avoiding inconvenient diagonal columns. (There are some high-profile buildings that use it, e.g. the Salk Institute in La Jolla, the HSBC building in Hong Kong.)
A triangle structure is significantly more rigid than a rectangular one. Vierendeel truss needs to be super rigid to resist flex. Not good for a bicycle.
In architecture it's sometimes called a Vierendeel truss, https://en.wikipedia.org/wiki/Vierendeel_bridge and it's very handy for avoiding inconvenient diagonal columns. (There are some high-profile buildings that use it, e.g. the Salk Institute in La Jolla, the HSBC building in Hong Kong.)