(b) A PIE (polygon with identified edges) can be represented as a word in which each symbol, x, occurs at most twice, either as an x and an x or as two copies of x. Symbols which occur only once represent unidentified edges and those that occur in a pair represent a pair of identified edges with x and x1 indicating an unlike pair and a couple of x's indicating a like pair. There is no significance in where the sequence begins. So a torus could be written as ab a+b1 or b aba and a Mbius Band as abac, baca etc. For each of the following draw the corresponding polygon with identified edges and use surgery (follow the steps in the proof of the Fundamental Theorem on Surfaces) to express it in the form mT+nD or mP+nD where D represents a disk, T represents a torus and P represents a projective plane. (b1) discontinuous (62) abc a 'ded b-1 (b) A PIE (polygon with identified edges) can be represented as a word in which each symbol, x, occurs at most twice, either as an x and an x or as two copies of x. Symbols which occur only once represent unidentified edges and those that occur in a pair represent a pair of identified edges with x and x1 indicating an unlike pair and a couple of x's indicating a like pair. There is no significance in where the sequence begins. So a torus could be written as ab a+b1 or b aba and a Mbius Band as abac, baca etc. For each of the following draw the corresponding polygon with identified edges and use surgery (follow the steps in the proof of the Fundamental Theorem on Surfaces) to express it in the form mT+nD or mP+nD where D represents a disk, T represents a torus and P represents a projective plane. (b1) discontinuous (62) abc a 'ded b-1