So what you're proposing mk, is essentially a box. I think you just invented modernism old boy! :)
Or a variation on the theme. :) When it comes to something that affects so much of your life, functionality needs to be fully satisfied. It's not as if it would run counter to his design goals. I bet he could roll that plastic into telescoping arches, and build something akin to this with less scrap and more space: There would be far less cutting involved.
This would require supports, as would your cube suggestion. His design requires none.
Ah yes. But a frame reduces the structural support to thin members - like a skeleton. This geodesic dome requires an overall homogenous assembly throughout. It spreads the structural capacity among its entire body, and as a result, becomes unnecessarily thick. The stick frame is more efficient since it localizes the bending moment. His geodesic dome is trying to work like a grid-shell design. And those too can be extremely efficient but only if the form is either catenary or some kind of pleated structure. Corrugated plastic just won't cut it - not to mention that putting in an operable window would prove challenging. Who needs natural air and light anyway?