The tesseract is the hypercube in 
, also called the 8-cell or octachoron. It has the Schläfli
symbol 
,
and vertices 
. The figure above shows a projection of
the tesseract in three-space (Gardner 1977). The tesseract is composed of 8 cubes
with 3 to an edge, and therefore has 16 vertices, 32 edges, 24 squares,
and 8 cubes. It is one of the six regular
polychora.
The tesseract has 261 distinct nets (Gardner 1966, Turney 1984-85, Tougne 1986, Buekenhout and Parker 1998).
In Madeleine L'Engle's novel A Wrinkle in Time, the characters in the story travel through time and space using tesseracts. The book actually uses the idea of a tesseract to represent a fifth dimension rather than a four-dimensional object (and also uses the word "tesser" to refer to movement from one three dimensional space/world 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 and 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 (or rather, the projection of a tesseract) out of popsicle sticks. In the Season 1 episode "Rampage" of the television crime drama NUMB3RS, main character mathematician Charlie Eppes discovers a popsicle-stick tesseract (projection) he built as a boy.
." Disc. Math. 186, 69-94, 1998.Coxeter,
H. S. M.