The right-angled cross motif we call the swastika has an ancient history as a good luck motif, before the Nazis appropriated it. In Japan, it is associated with Buddhist temples. The Japanese version usually faces left, whereas the Nazi swastika faces right. 

left and right facing

swastika

temple signifier

temple roof tile

manji motif

map indicating temples with manji

temple roof tile

swastika fretwork pattern