# History of Tesseract

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 Revision 9 . . (edit) November 18, 2001 6:07 pm by Zundark [copyediting] Revision 8 . . November 18, 2001 1:16 pm by Josh Grosse [Hopefully cleaned it up a bit, added some notes] Revision 7 . . November 18, 2001 11:57 am by (logged).144.199.xxx [Little tigher explanation] Revision 6 . . (edit) November 18, 2001 10:29 am by BF Revision 5 . . November 18, 2001 10:27 am by BF [You put a Greek character set codes in here. Restored and omitted symbol font for the non symbolic person. Leave the bold face alone !] Revision 4 . . (edit) November 18, 2001 9:56 am by (logged).12.199.xxx [added /talk] Revision 3 . . November 17, 2001 4:25 pm by Carey Evans [Change Symbol font to HTML 4 entities, + copyedit] Revision 2 . . November 17, 2001 3:13 pm by Josh Grosse [Rotating -> extruding] Revision 1 . . November 10, 2001 8:24 am by BF [4-D yes !]

Difference (from prior major revision) (minor diff, author diff)

Changed: 1c1,4
 A tesseract, also known as a hypercube, is a four dimensional object created by attaching an edge at each vertex of a cube such that these edges are oriented orthogonally to the other edges of the cube. Tesseracts inhabit a space with four dimensions, which is not easy for many people without mathematical training to visualize.
 A tesseract, or hypercube, is a four-dimensional analogue of a cube. In a square, each vertex has two perpendicular edges incident to it, while a cube has three. A hypercube has four. So, canonical coordinates for the vertices of a tesseract centered at the origin are (±1, ±1, ±1, ±1), while the interior of the same consists of all points (x0, x1, x2, x3) with -1 < xi < 1.

Changed: 3c6,11
 In a cube, every edge is shared by 2 squares. In a tesseract, 3 squares meet at every edge. A tesseract has 16 vertices, 32 edges, 24 squares, and 8 cubes.
 A tesseract is bound by eight hyperplanes, each of which intersects it to form a cube. Two cubes, and so three squares, intersect at each edge. There are three cubes meeting at every vertex, the vertex polyhedron of which is a regular tetrahedron. Thus the tesseract is given Schläfi notation {4,3,3}. All in all, it consists of 8 cubes, 24 squares, 32 edges, and 16 vertices. The square, cube, and tesseracts are all examples of measure polytopes in their respective dimensions.

Changed: 5,6c13,14
 A tesseract is defined by the set of points: {(x, y, z, h): 0 < x < 1, 0 < y < 1, 0 < z < 1, 0 < h < 1}
 External link: *http://pweb.netcom.com/~hjsmith/WireFrame4/tesseract.html has an illustration (requires Java).

Changed: 8,10c16,17