One Sided Surface in 4D

In the applet below, two repers - a pair of perpendicular segments - are randomly placed on one of 24 squares of the tesseract - a 4 dimensional cube or a hypercube. One 2D reper remains on that square for the duration of the experiment. The other reper can be moved to any of the 8 squares that have a common edge with the current one. (Obviously, there are 8 candidate squares, right?) The reper moves without rotation: if the two squares (the from-square and the to-square) were placed on the same plane, the reper would just glide from one to the other. The task is to take the moving reper on a ride at the end of which, back at the original square, the two repers will have different orientations.

The tesseract is the set of points

{(x,y,z,h): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, 0 ≤ z ≤ 1, 0 ≤ h ≤ 1}.

Its boundary cubes are defined by fixing value of one of the coordinates to either 0 or 1. This is why there are 8 of them. Each of the 24 squares is defined by fixing values of any two coordinates. There are 6 possible pairs and 4 possible values (00, 01, 10, 11) for each. Every square is assigned a 4 symbol name. X01H, for example, denotes the square for which y = 0 and z = 1.

alt="Your browser understands the <APPLET> tag but isn't running the applet, for some reason." Your browser is completely ignoring the <APPLET> tag!

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

What if applet does not run?


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