Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. The fourdimensional equivalent of a cube.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. The fourdimensional analogue of a cube; a 4D polytype bounded by eight cubes (in the same way a cube is bounded by six squares).
 n. Any of various fictional mechanisms that explain extradimensional, superluminal, or time travel outside the geometry of the physical universe.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. the fourdimensional analogue of a cube
Etymologies
Examples

It contains fourdimensional equivalents to our familiar threedimensional geometrical objectsa fourdimensional cube, for example, known as a tesseract, that has sixteen corners and thirtytwo edges to a cube's eight and twelve.

There's a theory of extradimensionality that holds that there are parallel universes as little as a mere .1 mm away from our own, but owing to the dimensions of our own universe (that is to say, it is folded over on itself like a sort of endless ribbon  think "tesseract" from "A Wrinkle in Time"), we are billions of lightyears away from the next nearest universe, as the crow flies.

Despite the fact that various advances made since 1962 in the field of physics make the scientific concept L’Engle uses to facilitate the novel’s events, called a tesseract, virtually impossible, A Wrinkle in Time remains a popular novel among young adults as well as older readers even today.

Thus the "fourdimensional cube" receives a name, the "tesseract," and is said to be bounded by cubes.

For instance, the projection of a cube may be made on to a plane, or even on to a line; similarly, a "tesseract" (the name given to the fourthdimension figure traced by the motion of a cube) may be projected on threedimension space, or even a plane.

Julian: Your desire for a dinghy is merely the tesseract shadow cast by the fourdimensional dinghy itself

In your spacetime version, when you reach this step, you need to grab the center of the structure and do the tesseract twist, wrench it round by about half a rad.
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Log in to Reply tesseract (UID#4004) on October 29th, 2009 at 3: 34 pm

Speaking of ways, by the way, there is such a thing as a tesseract.

I went over to the computer, entered tesseract UMBC Baltimore 1995, and found the report.
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oroboros commented on the word tesseract
A fourdimensional cube. Each face of a threedimensional cube generates a cube, when moved at right angles to the existing three dimensions (i.e., into time), including the generating cube and concluding cube, for a total of eight cubes. To see a twodimensional rendering, including fascinating moving images, click here.
Think of it as a cube that moves through time into the future. Also used as a symbol of transcendent vision.
March 17, 2007