Case (4). η : D 2 → S 2 defines a special almost orbifold covering of degree 4.

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... j * (S −1 2 · S 1 S 2 · S 2 ). As η * • j * = i * • η * and i * (S 1 S 2 ) = s 3 , we see that η * sends the generating pair (t 1 , t −ν 2 ) of π o 1 (O ) onto the pair T , and hence the special almost orbifold covering η : O → O represents the generating pair T . Case (4). In this case we have p 1 = 2, p 2 = 3 and p 3 4 with (p 3 , 3) = 1, and Fig. 5 (its precise description is given as in case (3)) and let O be the orifold with underlying surface D 2 and with two cone points y 1 and y 2 of order p 2 = 3 and p 3 respectively, i.e. O = D 2 (p 2 , p 3 ). Then η defines an almost orbifold covering of degree 4 from O to O. The description of η implies that η −1 (D) = D 1 C. The ...