Tesseract
A tesseract is a 4-dimensional object with eight cells. Each cell is a cube. Together, each cell makes the surface of the tesseract. Unlike three-dimensional objects which rotate on both an axis and a plane (the plane being two dimensions and the axis being of the leftover dimension, height), a tesseract rotates on two planes, one made up of two dimensions, and another made up of the other two dimensions.
It is not possible to make a tesseract out of real materials. A tesseract is in four dimensions, but we can only move in three dimensions.
A Line is to the 1st dimension, Square is to the 2nd dimension, Cube is to the 3rd dimension, Tesseract is to the 4th dimension.
Due to tesseracts being 4D, it is impossible to completely accurately render it in a 3D universe, on a 2D screen. This is similar to how projecting a 3d cube to make an image always causes distortions, except in 3D we don't notice.[1]
Tesseract Media
8-cell vertex figure.
The Dalí cross, a net of a tesseract
The tesseract can be unfolded into eight cubes into 3D space, just as the cube can be unfolded into six squares into 2D space.
An animation of the shifting in dimensions
A diagram showing how to create a tesseract from a point
Parallel projection envelopes of the tesseract (each cell is drawn with different color faces, inverted cells are undrawn)
The rhombic dodecahedron forms the convex hull of the tesseract's vertex-first parallel-projection. The number of vertices in the layers of this projection is 1 4 6 4 1—the fourth row in Pascal's triangle.
Animation showing each individual cube within the B4 Coxeter plane projection of the tesseract
Tesseract//16-cell family graph in B4 Coxeter plane
4-4 duoprism-isotoxal octagon projection
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References
- ↑ "Visualization". www.math.brown.edu. Retrieved 2025-01-04.