This is shown in the second step of the diagram. If you sweep out a distance equal to the length of the line, you will form a two-dimensional square. Now imagine taking hold of this line and sweeping it out in a direction perpendicular to its length. We form a one-dimensional line from a point by sweeping, or stretching, the point straight out in some direction. Let’s start from the zero-dimensional point and build our way up to the four-dimensional tesseract. To begin thinking about the relationship between tesseracts and cubes, it is helpful to consider the relation of cubes to squares, squares to lines, and lines to points. The tesseract is analogous to the cube in the same way that the cube is analogous to the square, the square to the line, and the line to the point. However, we can develop a general understanding of the tesseract by learning its structure, examining representations of the shape in lower dimensions, and exploring the math behind it.
![four dimensional hypercube four dimensional hypercube](https://i.ytimg.com/vi/-JLAxi2iKyc/maxresdefault.jpg)
As inhabitants of a three-dimensional world, we cannot fully visualize objects in four spatial dimensions. If you find this hard to picture, don’t worry.
![four dimensional hypercube four dimensional hypercube](https://c2.staticflickr.com/6/5206/5201850730_36d456f8be_b.jpg)
Instead of a cube’s eight corners, or vertices, a tesseract has sixteen. The sides of the four-dimensional tesseract are three-dimensional cubes. More specifically, it is the four-dimensional hypercube. The tesseract, or tetracube, is a shape inhabiting four spatial dimensions.
![four dimensional hypercube four dimensional hypercube](https://i.ytimg.com/vi/s0-XxHyla-8/maxresdefault.jpg)