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  2. Lists of uniform tilings on the sphere, plane, and hyperbolic ...

    en.wikipedia.org/wiki/Lists_of_uniform_tilings...

    There are 4 symmetry classes of reflection on the sphere, and three in the Euclidean plane. A few of the infinitely many such patterns in the hyperbolic plane are also listed. (Increasing any of the numbers defining a hyperbolic or Euclidean tiling makes another hyperbolic tiling.) Point groups:

  3. Spherical polyhedron - Wikipedia

    en.wikipedia.org/wiki/Spherical_polyhedron

    In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons. A polyhedron whose vertices are equidistant from its center can be conveniently studied by projecting its edges onto the sphere to obtain a corresponding ...

  4. Spherical cap - Wikipedia

    en.wikipedia.org/wiki/Spherical_cap

    An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.It is also a spherical segment of one base, i.e., bounded by a single plane.

  5. Gore (segment) - Wikipedia

    en.wikipedia.org/wiki/Gore_(segment)

    Red hot-air balloon, made from gores of material Single-use American WW II aircraft drop tanks, made of impregnated paper cylinders closed by gores formed into hemispheric shapes Globes of the Earth and the celestial sphere were first mass-produced by Johannes Schöner using a process of printing map details on 12 paper gores that were cut out ...

  6. Spherical geometry - Wikipedia

    en.wikipedia.org/wiki/Spherical_geometry

    The sum of the angles of a spherical triangle is not equal to 180°. A sphere is a curved surface, but locally the laws of the flat (planar) Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees. A sphere with a spherical triangle on it.

  7. List of spherical symmetry groups - Wikipedia

    en.wikipedia.org/wiki/List_of_spherical_symmetry...

    Finite spherical symmetry groups are also called point groups in three dimensions.There are five fundamental symmetry classes which have triangular fundamental domains: dihedral, cyclic, tetrahedral, octahedral, and icosahedral symmetry.

  8. Truncated icosahedron - Wikipedia

    en.wikipedia.org/wiki/Truncated_icosahedron

    The ball comprises the same pattern of regular pentagons and regular hexagons, each of which is painted in black and white respectively; still, its shape is more spherical. It was designed by Adidas Telstar during World Cup in 1970. [15] However, it was superseded in 2006. [16] The buckminsterfullerene molecule

  9. Geodesic polyhedron - Wikipedia

    en.wikipedia.org/wiki/Geodesic_polyhedron

    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, hemispherical architectural structures designed by Buckminster Fuller, which geodesic polyhedra are named after. Geodesic grids used in geodesy also have the geometry of geodesic polyhedra.

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