The strength of a triangle comes directly from its shape. Unlike many other shapes, which deform under even light loads, the triangle is very strong. In fact, a triangle cannot be deformed unless the length of one of its sides changes or one of its joints breaks. This fact has important implications in the engineering of many types of structures, including geodesic domes.

As in other applications such as bridge trusses, triangles connected to one another to form the shell of a dome provide incredible stability and strength relative to their weight. A geodesic dome, formed of many interconnecting triangles, may weigh only 1/300th what a solid dome of the same dimensions would weigh. Because of this, they can be made to enclose very large spaces. In fact, theoretically, there is no limit to the size of a geodesic dome.

An offshoot of the geodesic dome is the "tensegrity" structure. Tensegrity is a term used to refer to a concept called tensional integrity, where tension is distributed evenly and constantly across a large area. Like geodesic domes, tensegrity structures rely on triangles for their strength. Instead of simply enduring tension the way a geodesic dome does, tensegrity domes rely on constant tension along a system of cables connected to form triangles to hold the entire structure up. Rods attached to these cables at the vertices of the triangles hold up the roof of the dome and push downward on the cables. The cables, in turn, pull up on the rods, creating what is sometimes called a "dance" of tension and compression.

This very stable and lightweight system has been used to enclose very large spaces, including the Georgia Dome, a sports stadium that seats 50,000 people.