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In geometry, the tesseract, also called an 8cell or regular octachoron, is the fourdimensional analog of the cube. The tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of 6 square faces, the hypersurface of the tesseract consists of 8 cubical cells. The tesseract is one of the six convex regular 4polytopes.
A generalization of the cube to dimensions greater than three is called a "hypercube", "ncube" or "measure polytope". The tesseract is the fourdimensional hypercube, or 4cube.
According to the Oxford English Dictionary, the word tesseract was coined and first used in 1888 by Charles Howard Hinton in his book A New Era of Thought, from the Greek “τέσσερεις ακτίνες” (“four rays”), refernode_1 to the four lines from each vertex to other vertices. Some people have called the same figure a tetracube, and also simply a hypercube (although the term hypercube is also used with dimensions greater than 4).
Contents
Geometry
The tesseract can be constructed in a number of ways. As a regular polytope with three cubes folded together around every edge, it has Schläfli symbol {4,3,3}. Constructed as a 4D hyperprism made of two parallel cubes, it can be named as a composite Schläfli symbol {4,3} × { }. As a duoprism, a Cartesian product of two squares, it can be named by a composite Schläfli symbol {4}×{4}.
Since each vertex of a tesseract is adjacent to four edges, the vertex figure of the tesseract is a regular tetrahedron. The dual polytope of the tesseract is called the hexadecachoron, or 16cell, with Schläfli symbol {3,3,4}.
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