A nice cube is the Atomium. http://mathworld.wolfram.com/Cube.html
I propose that someone build a tetrahedron with vertices at 33.87 S, 151.20 E Sydney, Australia 24.80 S, 70.00 W northern Chile, S of Antofagasta 66.69 N, 151.70 W central Alaska, near Bettles Field 3.35 N, 39.92 E northeast Kenya (Thanks to Fred Helenius for identifying this "land tetrahedron": see http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/geographicals .) I picture something like the Atomium, with struts that disappear into the earth. Presumably the struts would terminate a few feet below the ground, although the viewer would be invited to imagine them as uninterrupted, several-thousand-mile-long beams. Who would pay for this? Well, if the struts are scaled-up version of the Zome construction system, the Zome guys might view the project as free advertising. Alternatively, the tetrahedron's latent It's-a-small-world-after-all, Building-bridges-between-nations political message might attract some potential funders of this conceptual art project. (To underscore the one-world theme, one could add video cams that let the viewers at each site watch what's happening at the other sites, along with a globe that shows the four vertices and the signal-paths that join them.) Or, maybe Sydney would fund the whole project, as a way of besting Melbourne? :-) Jim Propp