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0|0|0|||||Moebius-cut torus|David Bump|1|23:19:13|11/01/2008|I %22discovered%22 something I assumed had already been known%2C but I%27ve searched in vain for a site that stated it plainly and clearly. It%27s this%3A If you cut a solid toroidal body while making a half-twist %28following the path of an imaginary mobius strip embedded in the torus%29%2C the object remains in one piece%2C just as when cutting a mobius strip along its centerline. A true torus would also remain in one piece%2C but I think it is more dramatic with a common%2C solid body such as a donut. 
1|1|0|||||RE%3A Moebius-cut torus|alexb||08:37:38|11/09/2008|%3E... I think it is more dramatic with a common%2C solid %0D%0A%3Ebody such as a donut. %0D%0A%0D%0AYes%2C I agree. I do not remember seeing this mentioned. %0D%0A%0D%0AOne can start with flattening the torus%2C i.e. squeezing it %28or by chiseling away%29 to make a flat surface. This can be done in many ways%3B and getting a Moebius strip is one possibility. This done%2C you can cut the Moebius strip along the midline and then think of what this corresponds to on the original torus.%0D%0A%0D%0AThe trace of your %22knife%22 actually gives one possible flattening. The normal to that Moebius strip is the second %22knife%22 that produces the same result.%0D%0A%0D%0AVery nice. Thank  you.%0D%0A