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Most Goldberg polyhedra can be constructed using Conway polyhedron notation starting with (T)etrahedron, (C)ube, and (D)odecahedron seeds. The chamfer operator, c, replaces all edges by hexagons, transforming GP(m,n) to GP(2m,2n), with a T multiplier of 4.
This is a list of selected geodesic polyhedra and Goldberg polyhedra, two infinite classes of polyhedra. Geodesic polyhedra and Goldberg polyhedra are duals of each other. The geodesic and Goldberg polyhedra are parameterized by integers m and n , with m > 0 {\displaystyle m>0} and n ≥ 0 {\displaystyle n\geq 0} .
The discovery of Buckminsterfullerene in 1985 motivated research into other molecules with the structure of a Goldberg polyhedron. The terms "Goldberg–Coxeter fullerene" and "Goldberg–Coxeter construction" were introduced by Michel Deza in 2000. [13] [14] This is also the first time the degree 4 case was considered.
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 (which is a regular dodecahedron) have mostly hexagonal faces.
Goldberg polyhedra are made up of hexagons and (if based on the icosahedron) 12 pentagons. One implementation that uses an icosahedron as the base polyhedron, hexagonal cells, and the Snyder equal-area projection is known as the Icosahedron Snyder Equal Area (ISEA) grid.
A Goldberg polyhedron is a symmetric polyhedron constructed with hexagonal faces separating other polygons, usually pentagons in icosahedral symmetry. Pages in category "Goldberg polyhedra" The following 8 pages are in this category, out of 8 total.
It is a set of polyhedrons containing hexagonal and pentagonal faces. Other than two Platonic solids—tetrahedron and cube—the regular dodecahedron is the initial of Goldberg polyhedron construction, and the next polyhedron is resulted by truncating all of its edges, a process called chamfer. This process can be continuously repeated ...
In geometry, a polyhedron (pl.: polyhedra or polyhedrons; from Greek πολύ (poly-) 'many' and ἕδρον (-hedron) 'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set.