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 (x_{0}, x_{1}, x_{2}, x_{3}) with -1 < x_{i} < 1.

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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.

**External link:**

- http://pweb.netcom.com/~hjsmith/WireFrame4/tesseract.html has an illustration (requires Java).

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