In mathematical principle, I agree, triangles are good. In reality, because humans (from a front view, looking solely on a 2d plane) are more rectangle-shaped, generally, than triangle-shaped, it becomes difficult to design triangles around humans. Also, because gravity vectors tend to run at a 90 degree vertical orientation from the flat plane of the ground, it is more useful to have objects with a series of 90 degree bends so that you have one part upright and one part resting against the ground (a-la frames for doors, and indeed full houses). As someone else mentioned, hanging and trying to get through a triangular door would be horribly, needlessly complicated and would be a similarly difficult thing to mount properly so that it wouldn t slam shut the moment you opened it.
It could be
done, but why go through all those hurdles when you can just slap an 8 x4 rectangle in there and be done? Also, for things where you need to join things together and maintain a similar relative shape, I believe rectangles come out on top. Imagine trying to make a longer piece of paper if they were all triangular; you could do it once by gluing a bottom to a bottom, and then you have a diamond and can t expand downward without first expanding outward. Not only does a rectangle keep all of your margins justified and a consistent page-width, but if you need more length for something you can just glue another sheet to the bottom ad infinitum.
While I am a big fan of triangles in engineering (they make wonderful support structures for bridges and the like, and are an essential overall shape in aerodynamic design), for many purposes in most peoples everyday lives, rectangles are better suited. A tetrahedron composed of steel beams is very strong to shear forces, where a cube would easily collapse without other supports. On the other hand, when it comes to compression forces A cube will have four beams supporting each face and a tetrahedron would only have three. Even then, when a compression force is applied to a face, each steel beam in of itself is stronger to forces parallel to the the length of the beam versus perpendicular to its length.
A tetrahedron\’s supporting beams would be diagonal to the pressure and contrast with a cube\’s 4 support beams in parallel with the direction of force. Now when dealing with solids, and assuming the same random non crystalline internal structure between a tetrahedron and a cube, a tetrahedron sitting with one face on the ground will have one point facing up. The the tetrahedron highest point will be comparatively weak to oppose a compression force acting on it, and contrast with the same force applied to a much larger area of face of a cube. Both tetrahedron and cube would be about the same if the force is applied to it were applied to only a little point.