Mathematics Colloquia and Seminars

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Given regular r-graph G with edge chromatic number r, it is possible to construct an abstract r- Polytope P_G, such that the 1-squeleton of such polytope is the graph G. Turns out, that in the particular case when G is a path, P_G is the well known Permuthahedron. In this talk we will discuss this construction, give some examples of well known colorful polytopes such as the Colorful Associahedron and talk about interesting properties, such as natural embeddings of such polytopes in manifolds as well as its group of symmetries.