Question 2 (13 marks) (a) Take a rectangular strip of paper and put two half twists in it. Then glue the ends together. Call this object S. (Recall that the Mobius band has one half twist.) (i) Cut the object S lengthwise along the centre. Describe what you get. You may attach a photo. (ii) Explain why S is not equivalent by distortion to the Mobius band. (b) The object below on the left is what you get when you cut a hole out of a Klein bottle. You can also make the object using a net such as the one shown on the right (gluing along the arrows). One can draw two simple closed loops on this object that don't cross each other, such that cutting along both these loops still leaves the object in one piece. Draw these two loops on a net of the object. Question 2 (13 marks) (a) Take a rectangular strip of paper and put two half twists in it. Then glue the ends together. Call this object S. (Recall that the Mobius band has one half twist.) (i) Cut the object S lengthwise along the centre. Describe what you get. You may attach a photo. (ii) Explain why S is not equivalent by distortion to the Mobius band. (b) The object below on the left is what you get when you cut a hole out of a Klein bottle. You can also make the object using a net such as the one shown on the right (gluing along the arrows). One can draw two simple closed loops on this object that don't cross each other, such that cutting along both these loops still leaves the object in one piece. Draw these two loops on a net of the object