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The idea of fivedimensional space is an abstraction which occurs frequently in mathematics, where it is a legitimate construct. (In physics and mathematics, a sequence of N numbers can be understood to represent a location in an Ndimensional space.) Whether or not the real universe in which we live is somehow fivedimensional is a topic that is debated and explored in several branches of physics, including astrophysics and particle physics.^{[citation needed]}
In physics, the fifth dimension is a hypothetical extra dimension beyond the usual three spatial dimensions and one time dimension of Relativity. The Kaluza–Klein theory used the fifth dimension to unify gravity with the electromagnetic force. For example, Minkowski space and Maxwell's equations in vacuum can be embedded in a fivedimensional Riemann curvature tensor. Kaluza–Klein theory today is seen as essentially a gauge theory, with gauge group the circle group. Mtheory suggests that space–time has 11 dimensions, seven of which are "rolled up" to below the subatomic level. Physicists have speculated that the graviton, a particle thought to carry the force of gravity, may "leak" into the fifth or higher dimensions, which would explain how gravity is significantly weaker than the other three fundamental forces.^{[citation needed]}
In 1993, the physicist Gerard 't Hooft put forward the holographic principle, which explains that the information about an extra dimension is visible as a curvature in a spacetime with one fewer dimension. For example, holograms are threedimensional pictures placed on a twodimensional surface, which gives the image a curvature when the observer moves. Similarly, in general relativity, the fourth dimension is manifested in observable three dimensions as the curvature path of a moving infinitesimal (test) particle. Hooft has speculated that the fifth dimension is really the spacetime fabric.^{[citation needed]}
In five or more dimensions, only three regular polytopes exist. In five dimensions, they are:
A fourth polytope, a demihypercube, can be constructed as an alternation of the 5cube, and is called a 5demicube, with half the vertices (16), bounded by alternating 5cell and 16cell hypercells.
A_{5}  BC_{5}  D_{5}  

5simplex  5cube  5orthoplex  5demicube 
A hypersphere in 5space (also called a 4sphere due to its surface being 4dimensional) consists of the set of all points in 5space at a fixed distance r from a central point P. The hypervolume enclosed by this hypersurface is:
