Ypsi's Knights of Pythias was one of many fraternal groups in town. Others included the Masons, the Oddfellows, the Maccabees, the Phoenix Lodge, the Ancient Order of United Workmen, the Elks, the Catholic group the Knights of Columbus, and so on. Many Ypsilanti men were members of more than one group.
In Ypsi the Masons, the Oddfellows, and the Knights of Pythias among others had their own dedicated lodge meeting hall. You know where the Masonic one was; the K of P's was on the third floor of the old bank building at the southeast corner of Michigan Ave. and Huron (now City Hall). They met twice a month and shared the space with the Oddfellows.
The K of P was nationally founded in 1864. Wikipedia: "It was founded by Justus H. Rathbone, who had been inspired by a play by the Irish poet John Banim about the legend of Damon and Pythias. This legend illustrates the ideals of loyalty, honor and friendship that are central to the order."
Pythias, according to Greek legend, was a guy sentenced to death who asked to return home one last time. Dionysius [EDITED TO ADD: A king of Syracuse, not the god] granted his wish provided that he be chaperoned by Damon--and that if Pythias fled, Damon would be executed in his place. The day for Pythias to return came and went, and Dionysius was about to kill Damon when Pythias showed up at the last minute, saying that his ship had been delayed. Dionysius was so impressed by Pythias's loyalty that he pardoned both men and hired them.
Which may explain the vaguely Greek-ish dress of the group pictured here...but perhaps not the weird wildman pictured in back left. I'd like to know the story behind that. Click for full image.