5.06.2009

Tesseract (four-dimensional analog of the cube)

http://en.wikipedia.org/wiki/Tesseract
http://upload.wikimedia.org/wikipedia/commons/5/55/8-cell-simple.gifhttp://upload.wikimedia.org/wikipedia/commons/5/55/Tesseract.gif
[3D projections of an 8-cell performing, on the left, a simple rotation about a plane which bisects the figure from front-left to back-right and top to bottom; and on the right, a double rotation about two orthogonal planes.]

In geometry, the
tesseract, also called an 8-cell or regular octachoron, is the four-dimensional 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 4-polytopes.

A generalization of the cube to dimensions greater than three is called a ''Hypercube'', “n-cube” or “measure polytope”. The tesseract is the four-dimensional hypercube, or 4-cube.
According to the Oxford English Dictionary, the word tesseract was coined and first used in 1888 by Charles Howard Clinton in his book A New Era of Thought, from the Greek ''τέσσερεις ακτίνες'' (“four rays”), referring 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 a hypercube can be of any dimension).
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