We apply variations and extensions of structural balance theory to analyze the dynamics of geopolitical relations using data from the virtual world Eve Online. The highly detailed data enable us to study the interplay of alliance size, power, and geographic proximity on the prevalence and conditional behavior of triads built from empirical political alliances. Through our analysis, we reveal the degree to which the behaviors of players conform to the predictions of structural balance theory and whether our augmentations of the theory improve these predictions. In addition to studying the time series of the proportions of triad types, we investigate the conditional changes in triad types and the formation of polarized political coalitions. We find that player behavior largely conforms to the predictions of a multipolar version of structural balance theory that separates strong and weak configurations of balanced and frustrated triads. The high degree of explanatory power of structural balance theory in this context provides strong support for both the theory and the use of virtual worlds in social science research.