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  2. 3-sphere - Wikipedia

    en.wikipedia.org/wiki/3-sphere

    Direct projection of 3-sphere into 3D space and covered with surface grid, showing structure as stack of 3D spheres (2-spheres) In mathematics, a hypersphere or 3-sphere is a 4-dimensional analogue of a sphere, and is the 3-dimensional n-sphere. In 4-dimensional Euclidean space, it is the set of points equidistant from a fixed central point.

  3. File:3spheres.svg - Wikipedia

    en.wikipedia.org/wiki/File:3spheres.svg

    This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made ...

  4. Three spheres - Wikipedia

    en.wikipedia.org/wiki/Three_spheres

    Three spheres, triple spheres, and related terms may refer to any of the following: Architecture.

  5. Intersection (geometry) - Wikipedia

    en.wikipedia.org/wiki/Intersection_(geometry)

    There are two possibilities: if =, the spheres coincide, and the intersection is the entire sphere; if , the spheres are disjoint and the intersection is empty. When a is nonzero, the intersection lies in a vertical plane with this x-coordinate, which may intersect both of the spheres, be tangent to both spheres, or external to both spheres.

  6. 24-cell honeycomb - Wikipedia

    en.wikipedia.org/wiki/24-cell_honeycomb

    The cross-section of {3,4,3,3} by this hyperplane is a rectified cubic honeycomb. Each cuboctahedron in this honeycomb is a maximal cross-section of a 24-cell whose center lies in the plane. Meanwhile, each octahedron is a boundary cell of a (4-dimensional) 24-cell whose center lies off the plane.

  7. Spherical geometry - Wikipedia

    en.wikipedia.org/wiki/Spherical_geometry

    In the extrinsic 3-dimensional picture, a great circle is the intersection of the sphere with any plane through the center. In the intrinsic approach, a great circle is a geodesic; a shortest path between any two of its points provided they are close enough. Or, in the (also intrinsic) axiomatic approach analogous to Euclid's axioms of plane ...

  8. Homology sphere - Wikipedia

    en.wikipedia.org/wiki/Homology_sphere

    If p, q, and r are pairwise relatively prime positive integers then the link of the singularity x p + y q + z r = 0 (in other words, the intersection of a small 3-sphere around 0 with this complex surface) is a Brieskorn manifold that is a homology 3-sphere, called a Brieskorn 3-sphere Σ(p, q, r).

  9. Line–sphere intersection - Wikipedia

    en.wikipedia.org/wiki/Line–sphere_intersection

    No intersection at all; Intersection in exactly one point; Intersection in two points. Methods for distinguishing these cases, and determining the coordinates for the points in the latter cases, are useful in a number of circumstances. For example, it is a common calculation to perform during ray tracing. [1]