Per the Daily Iowan, the design is a replica of a parabolic radio telescope standing 20-feet tall was designed to turn 360 degrees horizontally and 90 degrees vertically. However, the chairman and designer that year said it would be unsafe for the vertical motion to be used.
The 1961 Homecoming Football Game was the Golden, or 50th, Anniversary of the first Homecoming Game where Iowa also played Wisconsin in 1912. The Daily Iowan reported that "One tradition that survived the last five decades is the building of a Homecoming monument. The first monument resembled a suspension bridge spanning Washington Street between the south end of the Physics building and the Engineering Building. Because the construction showed no visible means of support in the center, it was quite an attraction."
NASA's Gemini 1 was launched April 8, 1964 and this Corn Monument resembles the Gemini Capsule which was designed for a crew of 2. Gemini 1 was an uncrewed flight designed to test the new spacecraft and launch vehicle. The first crewed flight of the Project Gemini would come in 1965 with Gemini 3.
There was a snowstorm on October 26,1967 leaving 3 inches of snow before Homecoming Weekend Festivities were set to begin. Work was delayed on the monument construction - but students vowed it would be completed by Friday night, before the game.
This was not sponsored by the University, instead it was created by an anonymous student and placed on the Pentacrest where the monument would have been as the University did not create a monument that year. The Press Citizen cites a "new direction" on campus and the cost, "about $1000 a year plus $500 to resod the Pentacrest lawn after the monument is burned," as the causes for the tradition to be discontinued.
The 1966 Iowa Hawkeyes Football team was in the midst of a rebuilding period. Having gone 1-9 in 1965 and were heading into Homecoming 1966 with a 1-5 record. They would finish the 1966 season with a 2-8 record.
This monument was titled "Spartan's Reward" is straightforward in its symbolism - with the defeating of a Spartan that is reminiscent of the Battle of Thermopylae in 480 BCE. Of note is that the Hawkeye has the number "100" written across it. The first intercollegiate football game was on November 6, 1869 between Rutgers and Princeton and potentially the number "100" is a homage to that first game.