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Matschinski's identity and dual random tessellations

Various aspects of Matschinski's classical identity relating, in a homogeneous ergodic polygonal tessellation, the mean number of vertices, or sides, with the mean number of sides meeting at a random vertex, are discussed. It is shown how any such tessellation has a topological family of dual tessellations. An example given is that of an isotropic random tessellation, all of whose cells are quadrangles; another example has identical distributions of number of vertices and number of sides meeting at a vertex.