A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The rigid triangular elements of the dome distribute stress throughout the structure, making geodesic domes able to withstand very heavy loads for their size.
The Montreal Biosphère, formerly the American Pavilion of Expo 67, by R. Buckminster Fuller, on Île Sainte-Hélène, Montreal, Quebec
Spaceship Earth at Epcot
The Climatron greenhouse at Missouri Botanical Gardens, built in 1960 and designed by Thomas C. Howard of Synergetics, Inc., inspired the domes in the science fiction movie Silent Running.
Science World in Vancouver, built for Expo 86, and inspired by Buckminster Fuller's Geodesic dome.
A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex, except 12 vertices which have 5 triangles. They are the dual of corresponding Goldberg polyhedra, of which all but the smallest one have mostly hexagonal faces.
Image: Tetrakishexahedron
Image: Triakistetrahedron
Image: Order in chaos Magnus Wenninger