Fifth Dimension

In physics and mathematics, a string of N numbers, all in a row, can be understood to be 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, which, in the context of physics, refers to time, coming after the first three spatial dimensions (up/down, left/right and forwards/backwards). 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-dimensional geometry

A hexatetron, the 5-dimensional equivalent of a tetrahedron (or pyramid) has 6 vertices, 15 edges, 20 faces (each a triangle), 15 cells (or solids - each a tetrahedron), and 6 hypercells (each a pentachoron).

Related Topics:
Tetrahedron - Pentachoron

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A decatetron, the 5-dimensional equivalent of a hexahedron (or cube), has 32 vertices, 80 edges, 80 faces (each a square), 40 cells (each a cube), and 10 hypercells (each a tesseract).

Related Topics:
Hexahedron - Tesseract

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The volume of a 4-sphere (a 5-dimensional sphere) is:

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:V=rac{8pi ^2r^5}{15}

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