In the evolution of highway signs, the square or rectangular shape was first used to indicate any conditions which might affect driving on the highway. When it became necessary to differentiate between conditions along the right-of-way from conditions on the right-of-way, it was decided to rotate the square sign 45 degrees and let the diamond-shaped sign stand for curves, dips, hills, and other conditions on the roadway proper. Later, when a sign was needed to indicate STOP someone suggested cutting off the corners and making an octagonal sign of the diamond. The round sign was adopted as the designation for highway-railway crossings.
Proceedings of the Iowa Academy of Science
©1947 Iowa Academy of Science, Inc.
Lauer, A. R. and Embree, L. F.
"Certain Factors Affecting the Legibility of Stop Signs,"
Proceedings of the Iowa Academy of Science, 54(1), 243-245.
Available at: https://scholarworks.uni.edu/pias/vol54/iss1/37