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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.

Contents 1 Five dimensions in physics 2 Five-dimensional geometry 2.1 Polytopes 2.2 Hypersphere 3 The "Fifth dimension" in popular culture 4 See also 5 External links

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 forces. 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..

It has occasionally stated the fifth dimension is probability, meaning that the fifth dimension is the full amount of possibilities that could happen, in other words, alternate realities.

In five or more dimensions, only three regular polytopes exist. For N dimensions, they are:

1. 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).
2. The hypercubes, having 2^N vertices whose coordinates may be written (±1,±1, ..., ±1) for some suitable set of axes. It consists of 2N 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).
3. The cross polytope, with 2N 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:

Click any image to see a larger view

See also: 5-polytope, and List of regular 5-polytopes

The hypervolume of a Hypersphere in 5-space is:

• In the fictitious universe of DC Comics, the "Fifth dimension" is the place from which Mister Mxyzptlk comes.
• In 1966, The Byrds released an album entitled Fifth Dimension, in which the fifth dimension is a metaphor for unexplored and unknown aspects of the universe and oneself.
• The novel The Boy Who Reversed Himself features four and five-dimensional space, referred to as 4-space and 5-space.
• The hard science fiction novel Diaspora by Greg Egan features a series of ten dimensional universes arrayed inverse to one another, wherein every odd universe has four "macro" dimensions, three space plus one time, and six "submicro" dimensions, manifesting as a 6-sphere per every Planck distance, but which are themselves another ten dimensional universe, featuring six macro dimensions, five space plus one time, and four submicro dimensions per every Planck distance. A substantial portion of the novel depicts daily life and physics in such a universe, which differs substantially due to the peculiar physics hypothesis Egan formulated for the novel.
• Rod Serling's "The Twilight Zone" television series intro included the intro., "There is a Fifth Dimension, beyond that which is known to man."
• In the first episode of Doctor Who, Ian Chesterton was teaching his class about the three dimensions when Susan Foreman, his student and the Doctor's granddaughter, corrected him to say there were in fact five dimensions. He agreed the fourth was time, and asked her about the fifth, to which she replied it was 'space'.
• In the Hyperspace fictional book a series of 'Choose Your Own Adventure'
• The topic of 5-D being the "real world" has been displayed in the television series Smallville. In the show, it is observed that Mister Mxyzptlk has ordinary powers instead of powers of magic, hinting that the Superman of Smallville is the Superman of the fifth dimension or "real world."

• 5-manifold
• Hypersphere
• Dimension
• Fourth dimension

• www.tenthdimension.com - Simple educational tutorial exploring dimensions beyond the 5th. From the book "Imagining the Tenth Dimension" by Rob Bryanton.