The Sudanese Möbius band in the three-sphere "S"3 is geometrically a fibre bundle over a great circle, whose fibres are great semicircles. The most symmetrical image of a stereographic projection of this band into R3 is obtained by using a projection point that lies on that great circle that runs through the midpoint of each of the semicircles. Each choice of such a projection point results in an image that is congruent to any other. But because such a projection point lies on the Möbius band itself, two aspects of the image are significantly different from the case (illustrated above) where the point is not on the band: 1) the image in R3 is not the full Möbius band, but rather the band with one point removed (from its centerline); and 2) the image is unbounded – and as it gets increasingly far from the origin of R3, it increasingly approximates a plane. Yet this version of the stereographic image has a group of 4 symmetries in R3 (it is isomorphic to the Klein 4-group), as compared with the bounded version illustrated above having its group of symmetries the unique group of order 2. (If all symmetries and not just orientation-preserving isometries of R3 are allowed, the numbers of symmetries in each case doubles.)