Duality in Non-polyhedral Bodies Part II Triplets of the Polyliner

In a triplet group, there is a close relationship between three bodies, which in some respects is comparable to the relationship between two bodies in a dual pair. In both groups - dual pair and triplet - the bodies are completely equivalent to each other. Both or all three can serve as the starting point for the formation of the partner(s), whereby the same formation rule is applied. The phenomenon of triplets leads to connections between shapes and groups of shapes in a new, precise sense. The discovery of triplets is based on the introduction of polyliner, which result on the one hand from interpreting spherical graphs as solid bodies, and on the other hand from a generalization of polyhedra. Based on the application of the Conway transformations of polyhedron geometry to polyliner, the article introduces triplets: a group of three solids whose truncation and pyramid (Conway kis operator) forms are topologically identical. Furthermore, the edge set of the common truncation, resp., pyramid form is the disjoint union of the edge sets of the triplet.