“A geodesic dome is a sphere-like structure composed of a complex network of triangles. The triangles create a self-bracing framework that gives structural strength while using a minimum of material. The term geodesic is from Latin, meaning earth dividing. A geodesic line is the shortest distance between any two points on a sphere.”
http://architecture.about.com/od/domes/g/geodesic.htm
“A geodesic is the most economic relationship between any two events”
Buckminster Fuller
The Zeiss I planetarium in Jena designed by Walter Bauersfeld, constructed by ‘Dickerhoff and Widmann’ and opened in July 1926.
Buckminster Fuller with models of geodesic domes.
Domes have been constructed since ancient times. They form the basis of many vernacular typologies, such as wigwams and were employed by Romans as an architectural device on a grand scale to create monumental spaces. There have been many methods throughout history for dome construction, but geodesic domes are a product of the 20th century. They are easily recognisable and today evoke a certain ‘futuristic nostalgia’ yet it was a revolutionary design in its time.
Although it was first patented by Zeiss, it was Buckminster Fuller that really took ownership of this structural typology, developing the mathematics that underlie its structure and geometry (US paten 2682235 – 29 June 1954) as well as going to great lengths to advocate its use for all manner of building applications and programmatic needs.
Although Buckminster Fuller’s vision for the future application of his designs was quite utopic and never fully realised, he undoubtedly influenced the next generations of designers, engineers and architects. He inspired others to question the standard methodologies employed both in design thinking as well as construction techniques.
While the design of the dome has been realised in many different formats throughout the years, both at a smaller scale within the DIY build-your-own-home community and for greenhouses, it has also been used as the basis for much larger projects such as the Eden Project in Cornwall, UK designed by Nicholas Grimshaw.
Buckminster Fuller championed the efficiency, flexibility and resilience of the geodesic dome, but the legacy today is not just a pragmatic one. Artists, designers and architects have used the basic principles of geodesic domes as a canvas for their ideas to reinterpret its possible use.
N55, Urban Free Habitat System, 2008
Keg de Souza, Impossible Utopia
On Technology and Architecture 
There are various impacts to how we design relating to your post: “The triangles create a self-bracing framework that gives structural strength while using a minimum of material.” the notion of a self bracing framework, or the shortest distance between two points on a surface “A geodesic line is the shortest distance between any two points on a sphere.” We use them in generating grid shells, as there are other aspects of the notion of “geodesic” as can be found in Wolfram Math world; “Geodesics preserve a direction on a surface (Tietze 1965, pp. 26-27) and have many other interesting properties. The normal vector to any point of a geodesic arc lies along the normal to a surface at that point (Weinstock 1974, p. 65).”