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Unavoidable set of face types for planar maps

The type of a face f of a planar map is a sequence of degrees of vertices of f as they are encountered when traversing the boundary of f . A set T of face types is found such that in any normal planar map there is a face with type from T . The set T has four infinite series of types as, in a certain sense, the minimum possible number. An analogous result is applied to obtain new upper bounds for the cyclic chromatic number of 3-connected planar maps.