A hypercube, or tesseract, is a four-dimensional analogue of a cube. Just as a cube is made of square faces, a tesseract is made of cubical 'hyperfaces'. What you see here is a 3D projection of that 4D object.
The sliders below allow you to rotate the hypercube through different 4D planes. Each slider controls rotation in a plane involving the 'W' axis (the fourth dimension) and one of the familiar X, Y, or Z axes. Experiment with them to see how the hypercube's 3D shadow changes!