Tesseract

Charles Howard Hinton spent years attempting to develop ingenious methods by which the average person could "see" 4-dimensional objects. Eventually, Hinton perfected special cubes, that if one tried hard enough, could allow one to visualize a hypercube, or the 4-dimensional analogue to the cube. Hinton even cointed term for an unraveled hypercube. It is a tesseract. This name found its way into the English language. 

These cubes soon became of mystical importance, being advertised in women's magazines and even being used in seances. The claim by some members of high society was that you could catch glimpses of the 4th dimension from meditation on Hinton's cubes. Hence, one could get a glimpse of the netherworld or of the nearly departed. 

A hypercube cannot be visualized, however, its lower components can be unraveled. These are ordinary 3-dimensional cubes. 

The tesseract is the 4-dimensional analogue to the cube. The tesseract is to the cube as the cube is to the square. The surface of a cube consists of six square faces. In the same way, 

Charles Howard Hinton wrote an article in 1880. Hinton was fascinated with coming up with mathematical ways to visualize higher dimensional space, in particular, four-dimensional objects. Hinton coined the term "tesseract" to describe the analogue of a 4-dimensional cube. This is also known as a hypercube. 

We cannot visualize the hypercube, however, can unravel it's components. This unraveled hypercube would unfold into a kind of cross geometry, composed of 3-dimensional constituent cubes. Sadly, we cannot grasp how these cubes fold into a hypercube with our 3-dimensional minds.

We can also say that, in the same way that a 3-dimensional cube casts a 2-dimensional shadow: the shadow of a 4-dimensional tesseract would be a 3-dimensional cube within a cube. The shadow of a hypercube would be a cube within a cube.