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{\bf Catarina P. Avelino and Altino F. Santos}
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{\bf Spherical f-Tilings by Scalene Triangles and Isosceles Trapezoids III}
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The study of the dihedral f-tilings of the sphere $S^2$ whose
prototiles are a scalene triangle and an isosceles trapezoid was
initiated in parts I and II.  In this paper we complete this
classification presenting the study of all dihedral spherical
f-tilings by scalene triangles and isosceles trapezoids in the
remaining case of adjacency. A list containing all the f-tilings
obtained in this paper is presented. It is composed by isolated
tilings as well as discrete and continuous families of tilings. The
combinatorial structure is also achieved.

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