Bicyclic Star Polygons The applet explores turning bicyclic or poncelet polygons into star polygons.

The radio button under "points" to nominate the number of vertices in the polygons.
Tick the choice box under "skip" to determine the type of star polygon.
Each star polygon defines a new incircle. These all have one orthogonal circle which can be viewed by ticking the "show orthogonal circle" choice box.
The two buttons with "<" and ">" control the distance between the center of the outer circle and the first inner circle. When the distance is altered the program tries to make a new bicyclic polygon by altering the radius of the inner circle if it can not it rejects the new command. The result is pretty clunky but can be used to modify the polygons.
"show projection” makes a projection . See the applet “opposite intersects of bycylic polygons” for an explanation.
If you set the applet to 12 points and set all the skip buttons it hangs on some machines. The best way out is to exit the web page and restart.

A great link from Hungary
Eric W. Weisstein. "Poncelet's Porism." From MathWorld--A Wolfram Web Resource.
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