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The work is a detailed study of rational singularities of multiplicity 3(RTP-singularities, for short). We give a list of nonisolated hypersurfacesingularities of which normalisations are the RTP-singularities, and constructtheir minimal resolution graphs by means of a subdivision of Newton polygons ofthose -- a method introduced by M. Oka for isolated complete intersectionsingularities. We show that nonisolated forms of RTP-singularities and theirnormalisations are both Newton non-degenerate.

Nonisolated forms of rational triple point singularities of surfaces and their resolutions