Tesseract

3D projection of a tesseract, rotating along one axis

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]

Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron
Uniform 4-polytope 5-cell 16-cell • Tesseract Demitesseract 24-cell 120-cell • 600-cell
Uniform 5-polytope 5-simplex 5-orthoplex • 5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex • 6-cube 6-demicube 122 • 221
Uniform 7-polytope 7-simplex 7-orthoplex • 7-cube 7-demicube 132 • 231 • 321
Uniform 8-polytope 8-simplex 8-orthoplex • 8-cube 8-demicube 142 • 241 • 421
Uniform 9-polytope 9-simplex 9-orthoplex • 9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex • 10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplex • n-cube n-demicube 1k2 • 2k1 • k21 n-pentagonal polytope
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds

Preview of references

  1. ↑ "Visualization". www.math.brown.edu. Retrieved 2025-01-04.