Surfaces With Twists

no. of	   no. of	orientable	type of	     Results of cut:
 half	  boundaries   non-orientable	  cut	    no. of loops? length and
twists	   of the				    width? no. of twists? no.
	  surface				    of knots? orientable?


  0					center	


  0					one-third	


  1					center	


  1					one-third	 


  2					center	
 

  2					one-third	
 

  3					center	


  3					one-third	


  4					center	


  4					one-third	

Observations: