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This video and this image show a tesseract, which is a 4d cube:

tesseract

In what sense is this cube 4 dimensional? Where is time? (commonly called the 4th dimension, although I realize here its probably some sort of direction).

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    You are "seeing" a two dimensional model of a three dimensional model of a 4-dimensional figure. In four dimensions, any two edges meet at right angles; it's of course impossible to picture such an object in 3-dimensions, just like it is impossible to draw a cube in 2 dimensions in such a way that any two edges meet at right angles. You are seeing a projection of a projction.2011-08-03
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    Cube? Just looks like a bunch of 2D squares to me... ;)2011-08-03
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    In addition: mathematically, "time" is not "the fourth dimension"; "space time" is a particular physical model, but in mathematics, 4-dimensional Euclidean space is simply the set of all ordered 4-tuples $(a,b,c,d)$ with $a,b,c,d$ real numbers, satisfying certain axioms. Time doesn't enter into it.2011-08-03
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    If you looked at a still holographic projection of a 1x1x1 in^3 cube for 1 second, and identified 1 in = 1 sec, *then* you'd be seeing a tesseract using time as a "dimension." Although only one 3D cross-section of it at any given moment...2011-08-03
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    Nice animation! Who made it?2011-08-03
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    i think each of the eight cubes is a face of the tesseract2011-08-03
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    http://www.dimensions-math.org/Dim_E.htm is for you!2011-08-03
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    @yoyo: The terminology for three-dimensional polyhedra bounding a four-dimensional object is [cell](http://en.wikipedia.org/wiki/Cell_(mathematics)).2011-08-03
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    A segment of a square toroid between two meridians with a smoke-ring rolling,2017-04-08

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