The geometrical object that you can see on this page is called a tesseract. It is the 4D analogue of a cube. So what you see is rather a 3D shadow of a tesseract since humans have not yet found their way into the fourth dimension.

This shadow is created by stereographic projection from 4D to 3D. You can experiment with setting the origin of this projection. Or, alternatively, you can switch to orthographic projection. Note, however, that that's not the end! This webpage is 2D, so one more projection, this time a perspective projection, is applied, so that you can enjoy the tesseract on your screen.

Tesseract is composed of 8 cubes (similarly, a cube is composed of 6 squares and a square is composed of 4 line segments). You can change the color of any one of these cubes, so that it is easier to follow throughout the rotation.

Speaking of rotation, there are many options to choose from! Just like 2D space has one plane and 3D space has 3 planes, 4D space has 6 of them and you can have the tesseract rotate in each one of them. Or, you can have it rotate around two planes at once!

Enjoy!