Topological relations between spatial objects have played important roles in spatial representing and reasoning. Various models for expressing topological relations have been put forward. The Region Connection Calculus (RCC) and 9-Intersection Method (9IM) are most well-known topological formalisms, but neither of them can characterize the characteristic of topological relations between convex regions. In this paper, we introduce a new model for representing topological relations between two convex plane regions, which characterized with the topological properties of details of region A and B. Applying our model to triangles, we obtain a complete classification of topological relations which called RCC32. By calculating the cost of transforming one relation into another, the closest topological relation graph of RCC32 is given.