# Tesseracts: from 3 to 4 Dimensions.

The short video clip below shows the 3D rotations of a 4D object. The deeper questions concern the nature of a “dimension”. How do we know what a dimension is, and if we live in a 3D universe, could we possible also exist in a higher-dimensional universe? it is best to start with simple examples in order to train the mind to think about these questions. The clip below shows a tesseract, which is the four-dimensional analog of a cube. **(**In geomery, it is called** a regular octachoron** or **cubic prism**.) 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.

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**.

According to the Oxford English Dictionary, the word *tesseract* was coined and first used in 1888 by Charles Howard Hinton in his book *A New Era of Thought*, from the Greek τέσσερεις ακτίνες (“four rays”), referring to the four lines from each vertex to other vertices. Some people have called the same figure a **tetracube**, and also simply a **hypercube** (although the term hypercube is also used with dimensions greater than 4).