$$\tilde{A}$$ and $$\tilde{D}$$ type cluster algebras: triangulated surfaces and friezes

By viewing $$\tilde{A}$$ and $$\tilde{D}$$ type cluster algebras as triangulated surfaces, we find all variables in terms of either (i) the frieze pattern (or bipartite belt) or (ii) periodic quantities previously found for map associated with these patterns. We show that form friezes which are precisely ones by Assem–Dupont applying character to category.