Artificial intelligent assistant

What are the "garment thin" and the "prize" in the song "The Ballad of the Shape of Things to Come"? From the song "The Ballad of the Shape of Things to Come" (lyrics link): > Triangular is the piece of pie I eat to ease my sorrow > Triangular is the hatchet blade I plan to hide tomorrow > Triangular the relationship which now has ceased to be > And triangular is the **garment thin** > That fastens on with a safety pin > To a **prize I had no wish to win** > It's a lasting memory > That my true love gave to me I'm a non-native speaker, and the meaning is unclear to me. What could be this "garmet thin" of triangular shape? And what is the "prize I had no wish to win"? I feel that the two might be related so I clumped them into a single question. P.S. Who is the author of the ballad? I haven't found the author. The Kingston Trio?

Converting Robusto's comment to an answer:

The garment is a diaper, and the prize "I had no wish to win" is a baby.

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