First and Second Nearest Distances in Archimedean Tilings

Abstract

This paper provides the average and maximum distances to the first and second nearest vertices of Archimedean tilings. Distance is measured as the Euclidean distance. The distances in Archimedean tilings are useful for location analysis. The average distance can be used as a criterion of efficiency, whereas the maximum distance can be used as a criterion of equity. As an application to location analysis, we consider bi-objective problems where two distances are minimized. The result shows that tilings other than three regular tilings can be Pareto optimal.