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Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.
The regular complex polytope 4 {4} 2, , in has a real representation as a tesseract or 4-4 duoprism in 4-dimensional space. 4 {4} 2 has 16 vertices, and 8 4-edges. Its symmetry is 4 [4] 2, order 32. It also has a lower symmetry construction, , or 4 {}× 4 {}, with symmetry 4 [2] 4, order 16. This is the symmetry if the red and blue 4-edges are ...
Stereographic projection of the duocylinder's ridge (see below), as a flat torus.The ridge is rotating about the xw-plane.. The duocylinder, also called the double cylinder or the bidisc, is a geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks of respective radii r 1 and r 2:
In mathematics, the group of rotations about a fixed point in four-dimensional Euclidean space is denoted SO(4). The name comes from the fact that it is the special orthogonal group of order 4. In this article rotation means rotational displacement .
The 3-sphere is the boundary of a -ball in four-dimensional space. The ... Likewise, the stereographic projection of an ...
The space P n (K) is often called the projective space of dimension n over K, or the projective n-space, since all projective spaces of dimension n are isomorphic to it (because every K vector space of dimension n + 1 is isomorphic to K n+1). The elements of a projective space P(V) are commonly called points.
In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3); the special case for n = 4 is known as a tesseract.It is a closed, compact, convex figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, perpendicular to each other and of the same length.
Hermann Minkowski (1864–1909) found that the theory of special relativity could be best understood as a four-dimensional space, since known as the Minkowski spacetime.. In physics, Minkowski space (or Minkowski spacetime) (/ m ɪ ŋ ˈ k ɔː f s k i,-ˈ k ɒ f-/ [1]) is the main mathematical description of spacetime in the absence of gravitation.