A Tesseract is the four-dimensional equivalent of a cube.  In other words, according to http://mathworld.wolfram.com/Hypercube.html and http://mathworld.wolfram.com/Tesseract.html, a Tesseract is a four-dimensional hypercube (a regular cube being a three-dimensional hypercube).

The next candidate for a TetrisGame (since BlockOut already covered the 3D cube). ''I want to be the first on my block to own the display device for ''that'' game.''

Good point. Tetris up to the umpteenth dimension should be quite doable, except for the display. I can think of some workarounds, though - everything beyond 2D is a workaround anyway. Meanwhile, anyone for a game of 1D tetris?
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Actually, a tesseract can be visualized on-screen. It's fairly obvious when you consider the construction technique: ''Attach another cube to each face of a base cube, fold the attached cubes into the fourth dimension and put a cube in the space formed by the outer faces.'' 

The tesseract can be visualized as the eight cubes and the very neat movements between them. The most interesting part is how gravity behaves.

I've constructed a VR projection of a tesseract in AlphaWorld. Visitors Welcome at 1176N 37E. -- MarcThibault
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* http://tetraspace.alkaline.org/links-java.htm - neat JavaApplet tesseract things on the web
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CategoryMath