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  2. Geodesic polyhedron - Wikipedia

    en.wikipedia.org/wiki/Geodesic_polyhedron

    Geodesic subdivisions can also be done from an augmented dodecahedron, dividing pentagons into triangles with a center point, and subdividing from that Chiral polyhedra with higher order polygonal faces can be augmented with central points and new triangle faces. Those triangles can then be further subdivided into smaller triangles for new ...

  3. Geodesic dome - Wikipedia

    en.wikipedia.org/wiki/Geodesic_dome

    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.

  4. Goldberg–Coxeter construction - Wikipedia

    en.wikipedia.org/wiki/Goldberg–Coxeter...

    In geodesic dome terminology, this is the "breakdown structure" or "principal polyhedral triangle" (PPT). The 4-regular case uses the square lattice over the Gaussian integers, and the 3-regular case uses triangular lattice over the Eisenstein integers. For convenience, an alternate parameterization of the Eisenstein integers is used, based on ...

  5. Truncated icosahedron - Wikipedia

    en.wikipedia.org/wiki/Truncated_icosahedron

    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] In other engineering and science applications, its shape was also the configuration of the lenses used for focusing the explosive shock waves of the detonators in both the gadget and ...

  6. Category:Geodesic domes - Wikipedia

    en.wikipedia.org/wiki/Category:Geodesic_domes

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  7. Geodesic grid - Wikipedia

    en.wikipedia.org/wiki/Geodesic_grid

    Primarily, the cells' area and shape are generally similar, especially near the poles where many other spatial grids have singularities or heavy distortion. The popular Quaternary Triangular Mesh (QTM) falls into this category. [10] Geodesic grids may use the dual polyhedron of the geodesic polyhedron, which is the Goldberg polyhedron. Goldberg ...

  8. Geodesics on an ellipsoid - Wikipedia

    en.wikipedia.org/wiki/Geodesics_on_an_ellipsoid

    In order to find the relation for the third side AB = σ 12, the spherical arc length, and included angle N = ω 12, the spherical longitude, it is useful to consider the triangle NEP representing a geodesic starting at the equator; see Fig. 5. In this figure, the variables referred to the auxiliary sphere are shown with the corresponding ...

  9. Goldberg polyhedron - Wikipedia

    en.wikipedia.org/wiki/Goldberg_polyhedron

    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.