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2. Four-dimensional space - Wikipedia

   en.wikipedia.org/wiki/Four-dimensional_space

   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.

3. Spherinder - Wikipedia

   en.wikipedia.org/wiki/Spherinder

   The spherinder can be seen as the volume between two parallel and equal solid 2-spheres (3-balls) in 4-dimensional space, here stereographically projected into 3D.. In four-dimensional geometry, the spherinder, or spherical cylinder or spherical prism, is a geometric object, defined as the Cartesian product of a 3-ball (or solid 2-sphere) of radius r 1 and a line segment of length 2r 2:

4. Tesseract - Wikipedia

   en.wikipedia.org/wiki/Tesseract

   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 ...

5. 3-sphere - Wikipedia

   en.wikipedia.org/wiki/3-sphere

   while the 4-dimensional hypervolume (the content of the 4-dimensional region, or ball, bounded by the 3-sphere) is H = 1 2 π 2 r 4 . {\displaystyle H={\frac {1}{2}}\pi ^{2}r^{4}.} Every non-empty intersection of a 3-sphere with a three-dimensional hyperplane is a 2-sphere (unless the hyperplane is tangent to the 3-sphere, in which case the ...

6. A4 polytope - Wikipedia

   en.wikipedia.org/wiki/A4_polytope

   Three Coxeter plane 2D projections are given, for the A 4, A 3, A 2 Coxeter groups, showing symmetry order 5,4,3, and doubled on even A k orders to 10,4,6 for symmetric Coxeter diagrams. The 3D picture are drawn as Schlegel diagram projections, centered on the cell at pos. 3, with a consistent orientation, and the 5 cells at position 0 are ...

7. World line - Wikipedia

   en.wikipedia.org/wiki/World_line

   Unlike the present in Galilean/Newtonian theory, the elsewhere is thick; it is not a 3-dimensional volume but is instead a 4-dimensional spacetime region. Included in "elsewhere" is the simultaneous hyperplane, which is defined for a given observer by a space that is hyperbolic-orthogonal to their world line. It is really three-dimensional ...