4n-gons in the Poincare Disc

This demo shows a regular 4n-gon in the Poincare Disc. The tape deck changes the value of n, and the red hot spot changes the interior angles of the 4n-gon. The 'x' readout gives the interior angle in degrees. It is possible to find a position for the hot spot where the interior angles are 90 degrees, hence a regular right 4n-gon is constructable in the Poincare Disc.