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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. Sphere packing - Wikipedia

    en.wikipedia.org/wiki/Sphere_packing

    Sphere packing finds practical application in the stacking of cannonballs. In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space.

  4. Sphere - Wikipedia

    en.wikipedia.org/wiki/Sphere

    S ‍ 3: a 3-sphere is a sphere in 4-dimensional Euclidean space. Spheres for n > 2 are sometimes called hyperspheres. The n-sphere of unit radius centered at the origin is denoted S ‍ n and is often referred to as "the" n-sphere. The ordinary sphere is a 2-sphere, because it is a 2-dimensional surface which is embedded in 3-dimensional space.

  5. Point groups in three dimensions - Wikipedia

    en.wikipedia.org/wiki/Point_groups_in_three...

    Topologically, this Lie group is the 3-dimensional sphere S 3.) The preimage of a finite point group is called a binary polyhedral group , represented as l,n,m , and is called by the same name as its point group, with the prefix binary , with double the order of the related polyhedral group (l,m,n).

  6. n-sphere - Wikipedia

    en.wikipedia.org/wiki/N-sphere

    In mathematics, an n-sphere or hypersphere is an ⁠ ⁠-dimensional generalization of the ⁠ ⁠-dimensional circle and ⁠ ⁠-dimensional sphere to any non-negative integer ⁠ ⁠. The circle is considered 1-dimensional, and the sphere 2-dimensional, because the surfaces themselves are 1- and 2-dimensional respectively, not because they ...

  7. Three-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Three-dimensional_space

    Another type of sphere arises from a 4-ball, whose three-dimensional surface is the 3-sphere: points equidistant to the origin of the euclidean space R 4. If a point has coordinates, P ( x , y , z , w ) , then x 2 + y 2 + z 2 + w 2 = 1 characterizes those points on the unit 3-sphere centered at the origin.