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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 pentakis icosidodecahedron is a common geometry for geodesic domes derived from the icosahedron. Buckminster Fuller referred to it as the 2-frequency alternate geodesic subdivision of the icosahedron, because the edges are divided into 2 equal parts and then lengthed slightly to keep the new vertices on a geodesic great circle, creating a polyhedron with two distinct edge lengths and face ...
Those triangles can then be further subdivided into smaller triangles for new geodesic polyhedra. All vertices are valence-6 except the 12 centered at the original vertices which are valence 5. A geodesic polyhedron is a convex polyhedron made from triangles.
Geodesic dome (Montreal Biosphere, Canada) Geodesic domes are the upper portion of geodesic spheres. They are composed of a framework of triangles in a polyhedron pattern. [74] The structures are named for geodesics and are based upon geometric shapes such as icosahedrons, octahedrons or tetrahedrons.
The 31 great circles are shown here in 3 directions, with 5-fold, 3-fold, and 2-fold symmetry. There are 4 types of right spherical triangles by the intersected great circles, seen by color in the right image.
Geodesic domes are typically based on triangular facetings of this geometry with example structures found across the world, popularized by Buckminster Fuller. An example can be found in the model of a buckminsterfullerene, a truncated icosahedron-shaped geodesic dome allotrope of elemental carbon discovered in 1985. [17]