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In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces , the hypersurface of the tesseract consists of eight cubical cells , meeting at right angles .
Mar 28, 2021 · A tesseract or hypercube is the four-dimensional equivalent to a cube. In three dimensions, it is like a cube within a cube, except if all the vertices were connected by 90 degree angles. This animated GIF is a two-dimensional representation of a four-dimensional tesseract or hypercube.
A tesseract is also known as a hypercube or 8-cell. It is the 4D analog to the 2D square and the 3D cube. Its 3D "surface" is composed of 8 cubes, which enclose a 4D hypervolume. What is rendered here is not the actual tesseract, but its projection into 3D space in a process similar to photographing a 3D world onto 2D camera film.
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The hypercube is the special case of a hyperrectangle (also called an n-orthotope). A unit hypercube is a hypercube whose side has length one unit. Often, the hypercube whose corners (or vertices) are the 2 n points in R n with each coordinate equal to 0 or 1 is called the unit hypercube.
P =2P =3P =4P =5γ 2 2 = {4} = 4 verticesγ 3 2 = 9 verticesγ 4 2 = 16 verticesγ 5 2 = 25 verticesγ 2 3 = {4,3} = 8 verticesγ 3 3 = 27 verticesγ 4 3 = 64 verticesγ 5 3 = 125 verticesγ 2 4 = {4,3,3} = 16 verticesγ 3 4 = 81 verticesγ 4 4 = 256 verticesγ 5 4 = 625 verticesγ 2 5 = {4,3,3,3} = 32 verticesγ 3 5 = 243 verticesγ 4 5 = 1024 verticesγ 5 5 = 3125 verticesA tesseract, also known as a hypercube, is a four-dimensional cube, or, alternately, it is the extension of the idea of a square to a four-dimensional space in the same way that a cube is the extension of the idea of a square to a three-dimensional space.
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Jul 16, 2024 · Simply put, a tesseract is a cube in 4-dimensional space. You could also say that it is the 4D analog of a cube. It is a 4D shape where each face is a cube. A 3D projection of a tesseract performing a double rotation about two orthogonal planes.
