Hypercube
As used in geometry, a hypercube is an extrapolation of the cube or square to n dimensions. When n is not specified, it's generally assumed to be 4. For example, a 4th dimensional hypercube is called a tesseract. Therefore, an n-dimensional hypercube is also known as an n-cube. It is best drawn and represented in non-Euclidean geometry.
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Tesseract
A tesseract is the 4th dimensional hypercube. It is made by combining two cubes.
The net of a tesseract is composed of 8 cubes. It has the Schlaefli symbol 
. One simple coordinate system for its vertices are 
. The alternated tesseract is a 4D cross-polytope, which coincidentally, is also it's dual.
Extra Notes
The alternated hypercube is known as a demicube. The dual of the hypercube is known as the cross-polytope. For dimensions n≥3, the only n-dimensional regular honeycomb is made of the hypercube.
To see an 
xample of a 4D cube, click here: [1]
![[1]](https://latex.artofproblemsolving.com/3/d/5/3d5fc91ddaa1838f367ade6a2baa0649edd32317.png){kind=link}