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In Physics and Mathematics , a sequence of ''N'' numbers can be understood to represent a location in an ''N''-dimensional Space . When ''N''=5, one of these numbers is sometimes colloquially called the fifth dimension. This usage may occur in casual discussions about the Fourth Dimension . Abstract five-dimensional space occurs frequently in mathematics, and is a perfectly legitimate construct. Whether or not the real Universe in which we live is somehow five-dimensional is a topic that is debated and explored in several branches of physics, including Astrophysics and Particle Physics . FIVE DIMENSIONS IN PHYSICS In physics, the fifth dimension is a hypothetical extra dimension beyond the usual three Spatial and one Time dimensions. Some scientists 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 Force s. The Kaluza-Klein Theory used a fifth dimension to unify gravity with the Electromagnetic Force , and now is seen as essentially a Gauge Theory with Gauge Group the Circle Group . M-theory suggests that Space-time has Eleven Dimensions , seven of which are "rolled up" to below the sub-atomic level. 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 dimensions''. For example, holograms are three dimensional pictures placed on a two dimensional 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 of path of a moving infinitesimal (test) particle. Hooft has speculated that the fifth dimension is really the ''spacetime fabric''. FIVE-DIMENSIONAL GEOMETRY Polytopes In five or more dimensions, only three Regular Polytope s exist. For ''N'' dimensions, they are: # The Simplex , with ''N''+1 vertices, all at equal distances from one another; it consists of ''N''+1 simplices of dimension ''N''-1. The three-dimensional simplex is the Tetrahedron , and the five-dimensional simplex is a hexatetron; it has 6 vertices, 15 edges, 20 faces (each a Triangle ), 15 cells (or solids - each a Tetrahedron ), and 6 hypercells (each a Pentachoron ). # The Hypercube s, having 2''N'' vertices whose coordinates may be written (±1,±1, ..., ±1) for some suitable set of axes. It consists of 2''N'' hypercubes of the next lower dimension. The five-dimensional hypercube is a decateron or Penteract ; it has 32 vertices, 80 edges, 80 faces (each a Square ), 40 cells (each a Cube ), and 10 hypercells (each a Tesseract ). # The Cross Polytope , with 2''N'' vertices, paired on opposite sides of the ''N'' coordinate axes; it consists of 2''N'' Simplices of dimension ''N''-1. The five-dimensional cross polytope is a triacontakaiditeron or Pentacross , with 10 vertices, 40 edges, 80 faces (each a Triangle ), 80 cells (each a Tetrahedron ), and 32 hypercells (each a Pentachoron ). The Dual of a simplex is a simplex. The hypercube and cross-polytope of the same dimension are dual to each other. Here are three projected images of the edges of a regular decateron or Penteract : See also: 5-polytope , and List Of Regular 5-polytopes Hypersphere The hypervolume of a Hypersphere in 5-space is: : THE "FIFTH DIMENSION" IN POPULAR CULTURE
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