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.