Virgil Exner was nominally in charge of Chrysler styling when the 1960 redesign was underway. But he had suffered a major heart attack in 1956 that required open-heart surgery and a long recovery period. Because of this, Exner was not deeply involved with the design of cars under development during the late 1950s, nor was he always pleased with the results of the work done by others.
The subject of this post is the 1960 Plymouth Fury, a car with odd design features. Peter Grist, in his biography of Exner, has Cliff Voss responsible for its styling. Voss was an experienced designer who had held leadership positions for years, so I find it a bit strange that Plymouths appeared the way they did.
As it happened, Plymouth sales were not good during the 1960 model year. The 1961 facelift cleaned up the front end design somewhat, and tail fins were eliminated.