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Research Article Open Access
In this paper we introduced a new folding over a polygon we called it balanced folding, then we proved that for a balanced folding of a simply connected surface M there is a subgroup of the group of all homeomorphisms of M that acts 1-transitively on the 2-cells of M. Also we explored the relationship between balanced folding and covering spaces. Finally we obtained a general relation of the Euler number of surfaces which may balance folded over a polygon and we also listed all the possibilities if M is a sphere balanced folded over a triangle and we gave the subgroup mentioned above in each case.
Surface, Cellular folding, Singularities, Cayley color graph, 1-Transitive, Universal covering, Euler number, Smooth Complexities, Adomian Decomposition Method, Applied Mathematics, Number Theory, Sensitivity Analysis, Convection Diffusion Equations, Numerical Solutions, Nonlinear Differential Equations, Differential Transform Method , Balance Law, Quasilinear Hyperbolic Systems, Mixed Initial-boundary Value, Fuzzy Boundary Value, Semi Analytical-Solution, Integrated Analysis, Fuzzy Environments, Molecular Modelling, Fuzzy Quasi-Metric Space, Three Dimensional Steady State, Computational Model