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In five or more dimensions, only three regular polytopes exist. In five dimensions, they are: The 5-simplex of the simplex family, {3,3,3,3}, with 6 vertices, 15 edges, 20 faces (each an equilateral triangle), 15 cells (each a regular tetrahedron), and 6 hypercells (each a 5-cell).
However, the article does demonstrate that electromagnetism and gravity share the same number of dimensions, and this fact lends support to Kaluza–Klein theory; whether the number of dimensions is really 3 + 1 or in fact 4 + 1 is the subject of further debate.
[108] [109] [110] Temperament researchers point out that the lack of attention to surviving temperament research by the creators of the Big Five model led to an overlap between its dimensions and dimensions described in multiple temperament models much earlier.
The 5-cube can be projected down to 3 dimensions with a rhombic icosahedron envelope. There are 22 exterior vertices, and 10 interior vertices. The 10 interior vertices have the convex hull of a pentagonal antiprism. The 80 edges project into 40 external edges and 40 internal ones.
In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and 6 5-cell facets.It has a dihedral angle of cos −1 ( 1 / 5 ), or approximately 78.46°.
The 5th Dimension is an American vocal group. Their music encompasses sunshine pop, [1] pop soul, [1] and psychedelic soul. [2]Formed as the Versatiles in late 1965, the group changed its name to "the 5th Dimension" by 1966. [3]
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The topology of any given 5-polytope is defined by its Betti numbers and torsion coefficients. [1]The value of the Euler characteristic used to characterise polyhedra does not generalize usefully to higher dimensions, whatever their underlying topology.