About

In geometry, a tesseract, also called an 8-cell or regular octachoron or cubic prism or 4-cube or hypercube, is the four-dimensional analogue of the cube. The tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of 6 square faces, the hypersurface of the tesseract consists of 8 cubical cells. The tesseract is one of the six convex regular 4-polytopes. What you see in the picture to the right is the "cube-in-a-cube" model that is used to project it down to 2D, similar to how a cube can look like a square inside a square even though they aren't. The Tesseract is a Polychoron.

A generalization of the cube to dimensions greater than three is called a "hypercube", "n-cube" or "measure polytope". The tesseract is the four-dimensional hypercube, or 4-cube. Its 5D analogue is called a Penteract.

Formula

• Hypervolume: s⁴
• Surface Volume: 8s³

Gallery

2D Projection of the tesseract (note its not 3D)

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