Geodesic polyhedra

Geodesic polyhedron

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 with mostly hexagonal faces. Geodesic polyhedra are a good approximation to a sphere for many purposes, and appear in many different contexts. The most well-known may be the geodesic domes designed by Buckminster Fuller, which geodesic polyhedra are named after. Geodesic grids used in geodesy also have the geometry of geodesic polyhedra. The capsids of some viruses have the shape of geodesic polyhedra, and fullerene molecules have the shape of Goldberg polyhedra. Geodesic polyhedra are available as geometric primitives in the Blender 3D modeling software package, which calls them icospheres: they are an alternative to the UV sphere, having a more regular distribution of vertices than the UV sphere. The Goldberg–Coxeter construction is an expansion of the concepts underlying geodesic polyhedra. (Wikipedia).

Geodesic polyhedron
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Related pages

Icosahedral symmetry | Geodesic grid | Goldberg–Coxeter construction | List of geodesic polyhedra and Goldberg polyhedra | Face (geometry) | Tetrahedral symmetry | Rhombicosidodecahedron | Schläfli symbol | Vertex (geometry) | Dodecahedron | Degree (graph theory) | Equilateral triangle | Spherical polyhedron | Tetrahedron | Tessellation | Truncation (geometry) | Great circle | Icosahedron | Geodesic | Octahedral symmetry | Truncated icosahedron | Cube | Polyhedron | Polyhedral group | Polyhedron model | Regular dodecahedron | Sphere | Geometric primitive | Pentakis dodecahedron | Triangular tiling | Edge (geometry) | Conway polyhedron notation | Octahedron | Dual polyhedron