Spheres and tori that are bRj for

In this chapterwe present the classification of all ( a, b], 3)-spheres bRj for j 5. We also obtain the minimal such spheres for several cases. 

In order to prove (i), we take the following strictly face-regular ( 4,7, 31-plane 7R5 (belonging to Case 13 of Table 9.3)  

Note that there exist a ((4, 7, 3)-torus that is 4/fo but which is not 7R5. 

Lemma 18.1.2 Take a map G, such that its set T effaces is partitioned into two classes, T and T2, so that any face F in T is 6-gonal and adjacent to exactly five other faces of T. Then it holds that  

(i) follows from direct analysis of possible corona of faces. Given a face F 6 J 2. denote by N(F) the neighborhood of F in T (i.e. the set of all feces from T, which are adjacent to F). Clearly, the set T is partitioned into N(Fi),N(Fk). Suppose that two sets N(Fi) and N(Fj) have an adjacency. Then the following two cases are possible  

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