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Tesseract
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.
, 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.
SEE ALSO: Cube, Hypercube, Magic Tesseract, Polytope,
Simplex, Tesseract Graph
REFERENCES:
Referenced on Wolfram|Alpha: Tesseract
CITE THIS AS:
Buekenhout, F. and Parker, M. "The Number of Nets of the Regular Convex Polytopes in Dimension 
." Disc. Math. 186,
69-94, 1998.
." Disc. Math. 186,
69-94, 1998.
Coxeter, H. S. M. Regular
Polytopes, 3rd ed. New York: Dover, p. 123, 1973.
Dewdney, A. K. "Computer Recreations: A Program for Rotating Hypercubes Induces Four-Dimensional Dementia." Sci. Amer. 254, 14-23, Apr.
1986.
Fischer, G. (Ed.). Plate 4 in Mathematische Modelle aus den Sammlungen von Universitäten und Museen, Bildband. Braunschweig,
Germany: Vieweg, p. 5, 1986.
Gardner, M. "Mathematical Games: Is It Possible to Visualize a Four-Dimensional
Figure?." Sci. Amer. 214, 138-143, Nov. 1966.
Gardner, M. "Hypercubes." Ch. 4 in Mathematical Carnival: A New Round-Up of Tantalizers and Puzzles from Scientific American.
New York: Vintage Books, pp. 41-54, 1977.
Geometry Center. "The Tesseract (or Hypercube)." http://www.geom.umn.edu/docs/outreach/4-cube/.
L'Engle, M. A
Wrinkle in Time. Yearling, 1973.
Sawyer, R. Factoring
Humanity. New York: Orb Books, 2004.
Smith, H. J. "The Tesseract: A Look into 4-Dimensional Space." http://www.geocities.com/hjsmithh/WireFrame4/tesseract.html.
Tougne, P. "Combien de patrons un polyèdre peut-il avoir?" Pour
la Science, pp. 99-103, May 1986.
Turney, P. D. "Unfolding the Tesseract." J. Recr. Math. 17,
No. 1, 1-16, 1984-85.
Weimholt, A. "Tesseract Foldout." http://www.weimholt.com/andrew/tesseract.html.
Weisstein, Eric W. "Tesseract." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Tesseract.html
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