What is a tesseract?

In geometry, the tesseract is the four-dimensional analog of a cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells. The tesseract is one of the six convex regular 4-polytopes.

To better understand a tesseract, in Madeleine L'Engle's novel A Wrinkle in Time, the characters in the story travel through time and space using tesseracts. The book uses the idea of a tesseract to represent a fifth dimension rather than a four-dimensional object. It also uses the word "tesser" to refer to movement from one three dimensional space to another.

In the science fiction novel, Factoring Humanity by Robert J. Sawyer, a tesseract is used by humans on Earth to enter the fourth dimension. They contact another civilization on a planet orbiting the star Alpha Centauri A. The hypercube initially exists as a series of connected 3-dimensional cubes, which represent a hypercube that has been unfolded. Refolding the cube in a certain specific manner causes the reformation of the hypercube in 4 dimensions.

In John Mighton's play, Half Life, one of the characters (an aging mathematician) builds a tesseract (the projection of a tesseract) out of popsicle sticks. Finally, in the episode "Rampage" of the TV crime drama NUMB3RS, mathematician Charlie Eppes discovers a popsicle-stick tesseract (projection) he built as a boy.