Surfaces

This applet takes a polygon in R², with pairwise identification of the edges, and returns a closed surface in standard form, specifying its orientability, genus, and Euler characteristic.

If someone has any ideas about it, or eventually finds a bug, please feel free to contact me at inikolov@lynx.neu.edu Thank you.

Here are some points on the applet:

	Please, enter the sides in the format: *1, 2, -1, 2*... If you enter one side more than two times, the applet will not work even though it might be a closed surface.
	Normally in the final result the labels on the picture will have nothing to do with your labels.
	The applet will be working only if a correct closed (without any boundary) surface is entered. This is valid only if all of the sides entered are pairwise identified. e.g. if you enter '1' as a side of the polygon, you must enter once again (exactly once) '1' or '-1'.
	Note that in the result S stands for S², P stands for RP² and T stands for T²
	Check Show if you want to see the calculation step by step.
	The blue labels are the vertices and one can see them only if Show is checked.
	In the final drawing the yellow passages are toruses and the blue - projective planes.
	The algorithm for calculating is a seven-steps one. The Euler characteristic is calculated by the formula X = 2(1-g) for orientable and 2-h for non-orientable surfaces. What follows is a description of the algorithm.