Tesseract

To see how to construct a Tesseract - a 4 dimensional cube (often also, a hypercube) - press the Start button. The label on the button then converts to Continue. Keep pressing the Continue button to watch the successive steps of the construction. When finished, you'll be able to rotate the tesseract with sliders or by dragging the mouse. (You may also Skip the demonstration but remember that holding down the Shift or Control key changes the plane of rotation.)

The applet also shows the cross-section of the tesseract by a hyperplane given by the equation:

(Throughout, the fourth coordinate is denoted by h or H as a reminder that we deal with a hyperspace.)

Explanation