Abstract: Some results for the study of equivalent resistance of regularly connected polygon resistance network have already obtained, however, the study of unitive equivalent is still lacked if the parameter value （resistance or capacitor） in the polygon network is arbitrary constant. We analyze the network, construct a model based on difference equation and study unifying of equivalent resistance or capacitor of enhanced polygon network. We get a laconic general formula of equivalent resistance or capacitor of enhanced polygon network by analyzing the network, and obtain a simple expression of Fibonacci sequence in the meantime. We also expand the polygon concept arrives to two sides structure of the non-Euclid space. The results are compared with connected argument. The conclusion is also suitable to some regularly connected polygon impedance networks.

Key words: regular polygon, network analyze, equivalent resistance or capacitor, unify structure, non-Euclid space, Fibonacci sequence